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Journal articles on the topic 'Complex numbers interval'
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Lyra, Arão, Adrião Duarte Dória Neto, Benjamın René Callejas Bedregal, and Roque Mendes Prado Trindade. "A Polar Representation for Complex Interval Numbers." Revista de Ciência da Computação 1, no. 1 (March 29, 2019): 1. http://dx.doi.org/10.22481/recic.v1i1.4929.
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The present work defines the basic elements for the introduction to the Study of Complex variables under the mathematical interval context with the goal of using it as a foundation for the understanding of pure mathematical problems, associating the mathematical interval to support the results. The present article contributes to the complex interval theory taking into consideration Euler’s Identity and redefining the polar representation of interval complex numbers. In engineering, the present article could be used as a subsidy for many applications where complex variable theory is applicable and requires accurate results.
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Campos, Marcilia Andrade, and André Feitoza Mendonça. "Interval Enclosures for Reliability Metrics." TEMA (São Carlos) 17, no. 2 (September 4, 2016): 143. http://dx.doi.org/10.5540/tema.2016.017.02.0143.
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The computation of reliability metrics involves real numbers. Therefore, numerical problems are generated due to the limitation of representing and operating with real numbers in computers. This paper proposes interval functions for controlling numeric errors in the computation of reliability metrics values of complex systems, based on interval mathematics and high accuracy arithmetic. The interval functions calculate interval enclosures, using Intlab toolbox, for real values of reliability metrics and the SHARPE software was used to validate the results. Analysis of the numerical results obtained with the proposed functions showed that the intervals really enclose the real numbers calculated by the software SHARPE, indicating that these functions, in fact, are an alternative for auto-validating representation of these reliability values of complex systems.
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Kimberling, Clark. "Microcomputer-assisted mathematics: Roots: Half-Interval Search." Mathematics Teacher 78, no. 2 (February 1985): 120–23. http://dx.doi.org/10.5951/mt.78.2.0120.
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According to the fundamental theorem of algebra, the roots of a polynomial all lie in the set of complex numbers. Some of the roots may be real numbers, and in many applications, only these need be found.
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STANUJKIC, Dragisa. "AN EXTENSION OF THE RATIO SYSTEM APPROACH OF MOORA METHOD FOR GROUP DECISION-MAKING BASED ON INTERVAL-VALUED TRIANGULAR FUZZY NUMBERS." Technological and Economic Development of Economy 22, no. 1 (September 21, 2015): 122–41. http://dx.doi.org/10.3846/20294913.2015.1070771.
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Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers.
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Dai, Songsong, Lvqing Bi, and Bo Hu. "Distance Measures between the Interval-Valued Complex Fuzzy Sets." Mathematics 7, no. 6 (June 16, 2019): 549. http://dx.doi.org/10.3390/math7060549.
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Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.
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Dai, Songsong, Lvqing Bi, and Bo Hu. "Interval-Valued Complex Fuzzy Geometric Aggregation Operators and Their Application to Decision Making." Mathematical Problems in Engineering 2020 (July 22, 2020): 1–10. http://dx.doi.org/10.1155/2020/9410143.
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This paper investigates the geometric aggregation operators for aggregating the interval-valued complex fuzzy sets (IVCFSs) whose membership grades are a special set of complex numbers. We develop some geometric aggregation operators under the interval-valued complex fuzzy environment, namely, interval-valued complex fuzzy geometric (IVCFG), interval-valued complex fuzzy weighted geometric (IVCFWG), and interval-valued complex fuzzy ordered weighted geometric (IVCFOWG) operators. Then, we investigate the rotational and reflectional invariances of these operators. Further, a decision-making approach based on these operators is presented under the interval-valued complex fuzzy environment and an example is illustrated to demonstrate the efficiency of the proposed approach.
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Jiang, Wen, and Shiyu Wang. "An Uncertainty Measure for Interval-valued Evidences." International Journal of Computers Communications & Control 12, no. 5 (September 10, 2017): 631. http://dx.doi.org/10.15837/ijccc.2017.5.2950.
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Interval-valued belief structure (IBS), as an extension of single-valued belief structures in Dempster-Shafer evidence theory, is gradually applied in many fields. An IBS assigns belief degrees to interval numbers rather than precise numbers, thereby it can handle more complex uncertain information. However, how to measure the uncertainty of an IBS is still an open issue. In this paper, a new method based on Deng entropy denoted as UIV is proposed to measure the uncertainty of the IBS. Moreover, it is proved that UIV meets some desirable axiomatic requirements. Numerical examples are shown in the paper to demonstrate the efficiency of UIV by comparing the proposed UIV with existing approaches.
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Stanujkic, Dragisa, Nedeljko Magdalinovic, Rodoljub Jovanovic, and Sanja Stojanovic. "AN OBJECTIVE MULTI-CRITERIA APPROACH TO OPTIMIZATION USING MOORA METHOD AND INTERVAL GREY NUMBERS." Technological and Economic Development of Economy 18, no. 2 (June 29, 2012): 331–63. http://dx.doi.org/10.3846/20294913.2012.676996.
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Many real-world problems are complex and/or related to the manifestation of some form of uncertainty and/or prediction. Therefore the use of extended MCDM methods is more appropriate than the use of the other classic decision making methods. These methods are improved by the use of a form of fuzzy or interval grey numbers. In the field of operational research, during the previous period, numerous MCDM methods were formed, but one newly proposed, the MOORA method, is very specific and yet has no extension. Therefore, in this paper we combine concept of interval grey numbers and MOORA method in order to propose extended MOORA method which will be more appropriate to solve many complex real-world problems.
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Tang, Limin, and Xiuyan Zhao. "An Interval Parameter Calculation Method of Asphalt Pavement Structure Design Based on Point Numerical Algorithm." Advances in Civil Engineering 2021 (January 4, 2021): 1–11. http://dx.doi.org/10.1155/2021/8847180.
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In the asphalt pavement structure design method, the structural analysis and design are generally performed in the form of point values. However, determining the point value form of design parameters based on the statistical analysis theory cannot fully reflect the complex properties such as variability and uncertainty of parameters. In order to further improve the reliability and practicability of pavement design parameters, in this article, we have introduced the interval number representation that can better reflect the complex nature of parameters; but the interval number algorithm is too complicated and common calculation tools and software are difficult to adopt, which limit the wide application of interval analysis to some extent. The article analyzes the algorithm of interval numbers, focusing on the analysis of interval numbers of unary and binary functions. In this way, the point number operation can be used to obtain the interval number result of the function consistent with the interval number algorithm, which avoids the complicated interval number operation process and the interval expansion. The point numerical function algorithm of interval numbers is verified by design parameters and the calculation of asphalt pavement structure such as axle load conversion, cumulative equivalent axis calculation, calculation of foundation layer tensile stress of each structure layer, calculation of mixture penetration strength, fatigue cracking check of asphalt mixture layer, permanent deformation check, and vertical pressure strain test of roadbed top surface. In conclusion, this research provides a simple and easy way to implement the application of mathematical tools for interval analysis, which is suitable for direct use for existing point numerical calculation tools and software.
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Fallah, Mohammad, Amir Mohajeri, and Esmaeil Najafi. "Malmquist Productivity Index by Extended VIKOR Method Using Interval Numbers." Abstract and Applied Analysis 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/824316.
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The VIKOR method was developed for multicriteria optimization of complex systems. It determines the compromise ranking list and the compromise solution obtained with the given weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. Here, the VIKOR method is used for two timestandt+1. In order to calculate the progress or regression via Malmquist productivity index, the positive and negative ideals at timestandt+1are calculated first. Then we introduce the multi-criteria ranking index based on the particular measure of “closeness” to the ideal solution and calculate the separation of each alternative from the ideal solution at timestandt+1. Then we use the Malmquist productivity index to calculate the progress or regression of all alternatives. In this paper, productivity of alternatives available in decision matrix with interval numbers and their improvement or deterioration is researched. To achieve this practical goal, use of extended VIKOR is made to calculate Malmquist productivity index for multicriteria decision-making (MCDM) problem with interval numbers, and by applying Malmquist productivity index, productivity rate of growth for alternatives is calculated. Finally, a numerical example illustrates and clarifies the main results developed in this paper.
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Song, Haifeng, Lvqing Bi, Bo Hu, Yingying Xu, and Songsong Dai. "New Distance Measures between the Interval-Valued Complex Fuzzy Sets with Applications to Decision-Making." Mathematical Problems in Engineering 2021 (March 5, 2021): 1–9. http://dx.doi.org/10.1155/2021/6685793.
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As a generalization of complex fuzzy set (CFS), interval-valued complex fuzzy set (IVCFS) is a new research topic in the field of CFS theory, which can handle two different information features with the uncertainty. Distance is an important tool in the field of IVCFS theory. To enhance the applicability of IVCFS, this paper presents some new interval-valued complex fuzzy distances based on traditional Hamming and Euclidean distances of complex numbers. Furthermore, we elucidate the geometric properties of these distances. Finally, these distances are used to deal with decision-making problem in the IVCFS environment.
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Li, Tiejun, Jianhua Jin, and Chunquan Li. "Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers." Journal of Applied Mathematics 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/304287.
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Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems.
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Wang, Peng, Yang Li, Yong-Hu Wang, and Zhou-Quan Zhu. "A New Method Based on TOPSIS and Response Surface Method for MCDM Problems with Interval Numbers." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/938535.
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As the preference of design maker (DM) is always ambiguous, we have to face many multiple criteria decision-making (MCDM) problems with interval numbers in our daily life. Though there have been some methods applied to solve this sort of problem, it is always complex to comprehend and sometimes difficult to implement. The calculation processes are always ineffective when a new alternative is added or removed. In view of the weakness like this, this paper presents a new method based on TOPSIS and response surface method (RSM) for MCDM problems with interval numbers, RSM-TOPSIS-IN for short. The key point of this approach is the application of deviation degree matrix, which ensures that the DM can get a simple response surface (RS) model to rank the alternatives. In order to demonstrate the feasibility and effectiveness of the proposed method, three illustrative MCMD problems with interval numbers are analysed, including (a) selection of investment program, (b) selection of a right partner, and (c) assessment of road transport technologies. The contrast of ranking results shows that the RSM-TOPSIS-IN method is in good agreement with those derived by earlier researchers, indicating it is suitable to solve MCDM problems with interval numbers.
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Song, Shengyuan, Qiang Xu, Jianping Chen, Wen Zhang, Chen Cao, and Yongchao Li. "Engineering Classification of Jointed Rock Mass Based on Connectional Expectation: A Case Study for Songta Dam Site, China." Advances in Civil Engineering 2020 (May 20, 2020): 1–15. http://dx.doi.org/10.1155/2020/3581963.
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Engineering classification of complex jointed rock mass is influenced and controlled by many factors with random, nonlinear, and unascertained characteristics, which is an extremely complicated problem. This paper introduces a comprehensive method to classify the rock mass with complex joints. Firstly, evaluation indexes are described by the interval number theory. Secondly, the weight values of the evaluation indexes are determined by the analytic hierarchy process (AHP). Thirdly, the connectional expectation between interval numbers is analyzed and the classification grade of jointed rock mass quality is identified by the set pair analysis theory. The new method can not only describe the dynamic evolution trend of various influencing factors, but also simplify the analysis process of the relationship between interval numbers. The Songta dam abutment rock mass is selected as a study case to verify the rationality of the new method. The classification results of rock mass quality obtained by the new method are in accordance with the actual situation and are consistent with the results provided by the RMR classification.
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Park, Sang Woo, Kaiyuan Sun, David Champredon, Michael Li, Benjamin M. Bolker, David J. D. Earn, Joshua S. Weitz, Bryan T. Grenfell, and Jonathan Dushoff. "Forward-looking serial intervals correctly link epidemic growth to reproduction numbers." Proceedings of the National Academy of Sciences 118, no. 2 (December 23, 2020): e2011548118. http://dx.doi.org/10.1073/pnas.2011548118.
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The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.
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CORNFORTH, THEODORE W., and ANTHONY D. LONG. "Inferences regarding the numbers and locations of QTLs under multiple-QTL models using interval mapping and composite interval mapping." Genetical Research 82, no. 2 (April 2003): 139–49. http://dx.doi.org/10.1017/s0016672303006396.
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This paper examines the properties of likelihood maps generated by interval mapping (IM) and composite interval mapping (CIM), two widely used methods for detecting quantitative trait loci (QTLs). We evaluate the usefulness of interpretations of entire maps, rather than only evaluating summary statistics that consider isolated features of maps. A simulation study was performed in which traits with varying genetic architectures, including 20–40 QTLs per chromosome, were examined with both IM and CIM under different marker densities and sample sizes. IM was found to be an unreliable tool for precise estimation of the number and locations of individual QTLs, although it has greater power for simply detecting the presence of QTLs than CIM. The ability of CIM to resolve the correct number of QTLs and to estimate their locations correctly is good if there are three or fewer QTLs per 100 centiMorgans, but can lead to erroneous inferences for more complex architectures. When the underlying genetic architecture of a trait consists of several QTLs with randomly distributed effects and locations likelihood profiles were often indicative of a few underlying genes of large effect. Studies that have detected more than a few QTLs per chromosome should be interpreted with caution.
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Duan, Rongxing, Longfei Hu, and Yanni Lin. "Fault diagnosis for complex systems based on dynamic evidential network and multi-attribute decision making with interval numbers." Eksploatacja i Niezawodnosc - Maintenance and Reliability 19, no. 4 (September 21, 2017): 580–89. http://dx.doi.org/10.17531/ein.2017.4.12.
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PARISÉ, PIERRE-OLIVIER, and DOMINIC ROCHON. "TRICOMPLEX DYNAMICAL SYSTEMS GENERATED BY POLYNOMIALS OF ODD DEGREE." Fractals 25, no. 03 (May 2017): 1750026. http://dx.doi.org/10.1142/s0218348x17500268.
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In this paper, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial [Formula: see text] where [Formula: see text] and [Formula: see text] are complex numbers and [Formula: see text] is an odd integer. Furthermore, we show that the same Multibrots defined on the hyperbolic numbers are always squares. Moreover, we give a generalized 3D version of the hyperbolic Multibrot set and prove that our generalization is an octahedron for a specific 3D slice of the dynamical system generated by the tricomplex polynomial [Formula: see text] where [Formula: see text] is an odd integer.
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Mu, Runqing, Ke Yun, Xiaoou Yu, Shitong Cheng, Ming Ma, Xin Zhang, Shuo Wang, Min Zhao, and Hong Shang. "A study on reference interval transference via linear regression." Clinical Chemistry and Laboratory Medicine (CCLM) 58, no. 1 (December 18, 2019): 116–29. http://dx.doi.org/10.1515/cclm-2019-0055.
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Abstract Background Reference intervals (RIs) transference can expand the applicability of established RIs. However, the study on transference methodology is insufficient, and RIs validation based on small samples cannot adequately identify transferred risk under complex situations. This study aimed to find appropriate conditions to ensure the effect of transference. Methods We established the RIs of Roche and Beckman systems for 27 analytes based on 681 healthy individuals. Roche RIs were converted into the Beckman RIs using linear regression (least squares method) which is divided into two methods – Methodref (500 test numbers with relatively narrow data range) and Methodep (80 test numbers with relatively wide data range). Taking the RIs established by Beckman results as standard, we assessed the accuracy, precision and trueness of transferred results under various conditions. Results A total of 29.6% and 48.1% of analytes were consistent between the two systems for the lower and upper reference limits, respectively. The concordance rates between transferred and measured RIs for Methodref were up to 74.1% and 92.6%, which were better than Methodep (44.4% and 59.3%). The CV of transferred reference limits decreased gradually with increasing test number under the same data range. For most analytes, excluding some electrolyte tests, we could obtain accurate results when r > 0.800 and the test number was sufficient regardless of the regression equation types. Conclusions Transferability of RIs is affected by many factors, such as correlation, test number, regression equation type, and quality requirement. To reduce the risk of transference, it is very important to select right method with reasonable conditions.
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Baldwin, Stewart. "An extension of Šarkovskiư's Theorem to the n-od." Ergodic Theory and Dynamical Systems 11, no. 2 (June 1991): 249–71. http://dx.doi.org/10.1017/s0143385700006131.
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AbstractThe n-od is defined to be the set of all complex numbers z such that zn is a real number in the interval [0,1], i.e., a central point with n copies of the unit interval attached at their endpoints. Given a space X and a function f:X → X, Per (f) is defined to be the set {k: f has for a point of (least) period k, k a positive integer}. The main result of this paper is to give, for each n, a complete characterization of all possible sets Per (f), where f ranges over all continuous functions on the n-od.
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Ma, Jinshan, and Changsheng Ji. "Generalized Grey Target Decision Method for Mixed Attributes Based on Connection Number." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/763543.
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Grey target decision model for mixed attributes including real numbers, interval numbers, triangular fuzzy numbers, and trapezoidal fuzzy numbers is complex for its data processing in different ways and information distortion in handling fuzzy numbers. To solve these problems, the binary connection number proposed in set pair analysis is applied to unify different types of index values with their parameters’ average values and standard deviations as determinacy-uncertainty vectors. Then the target center index vectors are determined by the modules of index vectors of all alternatives under different attributes. So the similarity of each index vector and its target center index vector called nearness degree can be calculated. Following, all the nearness degrees are normalized in linear method in order to be compared with each other. Finally, the optimal alternative can be determined by the minimum of all integrated nearness degrees. Case study demonstrated that this approach can not only unify different types of numbers, and simplify the calculation but also reduce the information distortion in operating fuzzy numbers.
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Li, Lei, Xiaolu Xie, and Rui Guo. "Research on group decision making with interval numbers based on plant growth simulation algorithm." Kybernetes 43, no. 2 (February 25, 2014): 250–64. http://dx.doi.org/10.1108/k-07-2013-0138.
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Purpose – This paper aims at multi-attribute and multi-program group decision making when the attribute weights are completely unknown and the attribute value information is in the form of the interval number. Design/methodology/approach – This is an artificial intelligence algorithm for designing information gathering in group decision making. The authors propose the nonlinear programming model to gather information based on plant growth simulation algorithm (PGSA). The authors collect each program on each attribute group decision preference ordering interval and then use them to find the preference vector and the preference matrix. The entropy method is used to determine the weight of each attribute by the constructed preference matrix. According to the possibility degree matrix of each attribute, the combined effect vector is established by the priority weight vector method, which sorts and selects the best decision making program. Findings – To the authors' knowledge, the application of PGSA in the field of management decisions to collect program on each attribute group decision making preference interval number is the first trial in literature. It has retained more valuable decision making information from all experts without distortion. Practical implications – In practice, a real number may not be an accurate representation, but only gives a range of values to describe the attributes. This study provides a useful measurement of interval number information for managers to evaluate military science, venture capital, and environmental assessment, etc. Originality/value – The methodology considers the complete information to ensure no information distortion even with large and complex systems. The authors adopt computer artificial intelligence algorithms to obtain the objective evaluation, which is meaningful for both research studies and practical use.
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Garg, Harish, Zeeshan Ali, Zaoli Yang, Tahir Mahmood, and Sultan Aljahdali. "Multi-criteria decision-making algorithm based on aggregation operators under the complex interval-valued q-rung orthopair uncertain linguistic information." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 1627–56. http://dx.doi.org/10.3233/jifs-210442.
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The paper aims to present a concept of a Complex interval-valued q-rung orthopair uncertain linguistic set (CIVQROULS) and investigated their properties. In the presented set, the membership grades are considered in terms of the interval numbers under the complex domain while the linguistic features are added to address the uncertainties in the data. To further discuss more, we have presented the operation laws and score function for CIVQROULS. In addition to them, we present some averaging and geometric operators to aggregate the different pairs of the CIVQROULS. Some fundamental properties of the proposed operators are stated. Afterward, an algorithm for solving the decision-making problems is addressed based on the proposed operator using the CIVQROULS features. The applicability of the algorithm is demonstrated through a case study related to brain tumors and their effectiveness is compared with the existing studies.
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Su, Weihua, Shouzhen Zeng, and Xiaojia Ye. "UNCERTAIN GROUP DECISION-MAKING WITH INDUCED AGGREGATION OPERATORS AND EUCLIDEAN DISTANCE." Technological and Economic Development of Economy 19, no. 3 (October 3, 2013): 431–47. http://dx.doi.org/10.3846/20294913.2013.821686.
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In this paper, we present the induced uncertain Euclidean ordered weighted averaging distance (IUEOWAD) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the Euclidean distance and uncertain information represented by interval numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision-maker by using order-inducing variables in the aggregation of the Euclidean distance. Moreover, it is able to deal with uncertain environments where the information is very imprecise and can be assessed with interval numbers. We study some of its main properties and particular cases such as the uncertain maximum distance, the uncertain minimum distance, the uncertain normalized Euclidean distance (UNED), the uncertain weighted Euclidean distance (UWED) and the uncertain Euclidean ordered weighted averaging distance (UEOWAD) operator. We also apply this aggregation operator to a group decision-making problem regarding the selection new artillery weapons under uncertainty.
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Ren, Kun, and Qu Jihong. "A Multiobjective Interval Programming Model for Wind-Hydrothermal Power System Dispatching Using 2-Step Optimization Algorithm." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/825216.
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Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision.
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Nayagam, V. Lakshmana Gomathi, and Jagadeeswari Murugan. "Hexagonal fuzzy approximation of fuzzy numbers and its applications in MCDM." Complex & Intelligent Systems 7, no. 3 (February 16, 2021): 1459–87. http://dx.doi.org/10.1007/s40747-020-00242-4.
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AbstractNumerous research papers and several engineering applications have proved that the fuzzy set theory is an intelligent effective tool to represent complex uncertain information. In fuzzy multi-criteria decision-making (fuzzy MCDM) methods, intelligent information system and fuzzy control-theoretic models, complex qualitative information are extracted from expert’s knowledge as linguistic variables and are modeled by linear/non-linear fuzzy numbers. In numerical computations and experiments, the information/data are fitted by nonlinear functions for better accuracy which may be little hard for further processing to apply in real-life problems. Hence, the study of non-linear fuzzy numbers through triangular and trapezoidal fuzzy numbers is very natural and various researchers have attempted to transform non-linear fuzzy numbers into piecewise linear functions of interval/triangular/trapezoidal in nature by different methods in the past years. But it is noted that the triangular/trapezoidal approximation of nonlinear fuzzy numbers has more loss of information. Therefore, there is a natural need for a better piecewise linear approximation of a given nonlinear fuzzy number without losing much information for better intelligent information modeling. On coincidence, a new notion of Generalized Hexagonal Fuzzy Number has been introduced and its applications on Multi-Criteria Decision-Making problem (MCDM) and Generalized Hexagonal Fully Fuzzy Linear System (GHXFFLS) of equations have been studied by Lakshmana et al. in 2020. Therefore, in this paper, approximation of nonlinear fuzzy numbers into the hexagonal fuzzy numbers which includes trapezoidal, triangular and interval fuzzy numbers as special cases of Hexagonal fuzzy numbers with less loss/gain of information than other existing methods is attempted. Since any fuzzy information is satisfied fully by its modal value/core of that concept, any approximation of that concept is expected to be preserved with same modal value/core. Therefore, in this paper, a stepwise procedure for approximating a non-linear fuzzy number into a new Hexagonal Fuzzy Number that preserves the core of the given fuzzy number is proposed using constrained nonlinear programming model and is illustrated numerically by considering a parabolic fuzzy number. Furthermore, the proposed method is compared for its efficiency on accuracy in terms of loss of information. Finally, some properties of the new hexagonal fuzzy approximation are studied and the applicability of the proposed method is illustrated through the Group MCDM problem using an index matrix (IM).
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Persinger, M. A. "Clinical Neurological Indicators are Only Moderately Correlated with Quantitative Neuropsychological Test Scores in Patients Who Display Mild-Moderate Brain Impairment following Closed-Head Injuries." Perceptual and Motor Skills 81, no. 3_suppl (December 1995): 1283–92. http://dx.doi.org/10.2466/pms.1995.81.3f.1283.
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Quantitative comparisons were completed between mean scores for standardized neuropsychological tests (requiring 6 hr.), numbers of neurological signs (tests requiring 15 min.), anomalies within the electroencephalogram, subjective symptoms during a structured interview (requiring 20 min.), and an indicator of an organic brain syndrome for 81 patients who had sustained significant mechanical impacts to their skulls. The composite of neuropsychological scores was correlated 0.70 with a composite of neurological indicators and EEG anomalies. There were no significant correlations between neuropsychological or neurological scores and the numbers of subjective complaints, abnormal personality indicators, duration of coma or the interval of posttraumatic dysmnesia. However, the scores for the severity of the organic brain syndrome, partial complex epileptic symptoms, and subjective complaints were inversely correlated ( rho = −0.35) with the duration of coma, the period of posttraumatic amnesia, and the numbers of qualitative electroencephalographic anomalies.
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Bajger, Mariusz, Janusz Brzdęk, El-sayed El-hady, and Eliza Jabłońska. "On the Continuous Cancellative Semigroups on a Real Interval and on a Circle and Some Symmetry Issues." Symmetry 12, no. 12 (November 29, 2020): 1974. http://dx.doi.org/10.3390/sym12121974.
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Let S denote the unit circle on the complex plane and ★:S2→S be a continuous binary, associative and cancellative operation. From some already known results, it can be deduced that the semigroup (S,★) is isomorphic to the group (S,·); thus, it is a group, where · is the usual multiplication of complex numbers. However, an elementary construction of such isomorphism has not been published so far. We present an elementary construction of all such continuous isomorphisms F from (S,·) into (S,★) and obtain, in this way, the following description of operation ★: x★y=F(F−1(x)·F−1(y)) for x,y∈S. We also provide some applications of that result and underline some symmetry issues, which arise between the consequences of it and of the analogous outcome for the real interval and which concern functional equations. In particular, we show how to use the result in the descriptions of the continuous flows and minimal homeomorphisms on S.
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Luo, Shu Xin, Jing Li, and Fa Chao Li. "Synthesizing Effect Model Based on Quasi-Linear Function in Intelligent Materials System." Applied Mechanics and Materials 63-64 (June 2011): 29–32. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.29.
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Interval number is a common tool to describe uncertain information. Its ranking method plays a role in solving uncertain decision-making problems. In Ref. [1], by analyzing the feature and shortcomings of the current ranking methods, we proposed a ranking method based on quantity property, and systematically discussed the structure criteria, based on it, in this paper, we firstly introduce the definition of quasi-linear function and establishan order model of interval numbers based on it; secondly, with a specific example, we further analysis the property the order structure built in Ref. [1]. The result shows that this method can merge decision making consciousness into the decision making process effectively. In complex optimization system, decision making and other fields have a wide range of applications.
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Li, Aihua, and Zhangyan Zhao. "An Improved Model of Variable Fuzzy Sets with Normal Membership Function for Crane Safety Evaluation." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/3190631.
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Crane safety evaluation is significant for reducing the casualties and economic losses. Various evaluation methods have been applied to evaluate crane safety. However, when index standard with respect to every level is described in terms of intervals, existing crane safety evaluation models are not ideal. Although variable fuzzy sets (VFS) method has successfully solved similar problems, its evaluation processes are rather complex complicated and tedious. In this paper, we provided an improved VFS evaluation method with normal membership function for solving crane safety problem, in which the evaluation criteria are described in terms of intervals. To demonstrate our presented method, the improved variable fuzzy sets (IVFS) method was applied to two numerical cases including an application to crane safety assessment. It is shown that our proposed method possesses the merit to simplify assessment processes of traditional VFS and can be applied to assess crane safety when criteria values are defined as interval numbers.
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Waterstrat, Amanda J., Ying Liang, Hartmut Geiger, and Gary Van Zant. "Slit2 Increases Hematopoietic Stem Cell Numbers in Mice." Blood 112, no. 11 (November 16, 2008): 77. http://dx.doi.org/10.1182/blood.v112.11.77.77.
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Abstract A complex interaction of cell-intrinsic and extra-cellular signals cooperate to determine the number and behavior of Hematopoietic Stem Cells (HSCs). Elucidation of these regulatory networks promises to offer novel insights into HSC biology and HSC-mediated clinical therapies. In an effort to identify cell-intrinsic, genetic regulatory mechanisms determining HSC number, we initiated a forward genetic analysis beginning with HSC quantification in inbred mice using the Cobblestone Area Forming Cell (CAFC) assay. Subsequent linkage analysis revealed that the 3–7 fold larger HSC population in young DBA/2 relative to C57BL/6 mice was linked to multiple quantitative trait loci (QTL), including a locus with peak linkage (LOD = 3.1) at the 40 Mb position on chromosome 5 with a 95% confidence interval ranging from 29.3–55 Mbp. Congenic strains were generated on both the C57BL/6 and DBA/2 backgrounds in which the chromosome 5 QTL was exchanged between the strains by selective, genotype-assisted breeding. The DBA/2 interval increased HSC number 2.4 fold relative to the C57BL/6 background strain while the C57BL/6 QTL decreased HSC number 2 fold relative to the DBA/2 strain. Gene expression profiling of Lineage negative, Sca-1+, c-Kit+ (LSK) cells from C57BL/6, DBA/2 and congenic mice revealed 6 differentially expressed candidate genes in the 95% confidence interval among the 46,644 probes on the array. Among them a single transcript, Slit2, was expressed in a pattern correlated with stem cell number in both congenic-background strain comparisons and could be verified by RT-PCR analysis. Slit2 expression was positively correlated with HSC number and highly enriched in LSK cells of inbred and congenic mice bearing the DBA/2 genotype at the chromosome 5 QTL. A retrovirus was used to stably infect HSC-enriched C57BL/6 bone marrow cells, which normally do not express Slit2, with a Slit2-containing GFP vector, resulting in ectopic expression of the Slit2 transcript in GFP+ cells. Infected cells were then transplanted into sub-lethally irradiated C57BL/6 hosts and expanded in vivo for 12 weeks ensuring reconstitution of the complete hematopoietic hierarchy within the GFP+ fraction. CAFC analysis of GFP+ cells revealed that the ectopic expression of Slit2 resulted in a 2-fold increase in HPC/HSC numbers relative to an empty vector control. On the basis of this finding we demonstrate for the first time that expression of Slit2 by HSCs results in expansion of the HSC population. Slit/Roundabout (Robo) signaling is required in embryonic and neuronal development and has recently been shown to play important roles in the migration and function of a growing list of non-neuronal cells including a variety of cancer cell types. Future studies will aim to determine if Slit2 expression influences the interaction between HSCs and the microenvironment in a manner that promotes expansion of the HSC compartment, perhaps by overriding quiescence cues from the niche and/or altering the spatial orientation of stem cells within the bone marrow microenvironment.
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Faizi, Shahzad, Wojciech Sałabun, Samee Ullah, Tabasam Rashid, and Jakub Więckowski. "A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique." Symmetry 12, no. 4 (April 2, 2020): 516. http://dx.doi.org/10.3390/sym12040516.
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Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the pivotal challenge of rank reversal paradox and is proficient at handling vagueness and hesitancy. Classical COMET is not designed for handling uncertainty data when the expert has a problem with the identification of the membership function. In this paper, symmetrical and asymmetrical normalized interval-valued triangular fuzzy numbers (NIVTFNs) are used for decision-making as the solution of the identified challenge. A new MCDM method based on the COMET method is developed by using the concept of NIVTFNs. A simple problem of MCDM in the form of an illustrative example is given to demonstrate the calculation procedure and accuracy of the proposed approach. Furthermore, we compare the solution of the proposed method, as interval preference, with the results obtained in the Technique for Order of Preference by Similarity to Ideal solution (TOPSIS) method (a certain preference number).
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Wang, Xingang, and Ke Wang. "A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method." Journal of Intelligent & Fuzzy Systems 40, no. 1 (January 4, 2021): 221–33. http://dx.doi.org/10.3233/jifs-191261.
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In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS∖ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct.
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Fan, Yun, Zhigeng Fang, Sifeng Liu, and Jun Liu. "A grey approach to site selection for nursing homes: An extension of the fuzzy analytic hierarchy process." Journal of Intelligent & Fuzzy Systems 40, no. 5 (April 22, 2021): 8807–18. http://dx.doi.org/10.3233/jifs-200480.
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The construction of more nursing homes has become one of the most needed pension services in China, and the issue of site selection is one of the most important steps in their construction. The problem of site selection for nursing homes is a complex system engineering problem that involves not only economic interests but also social interests. Due to the limitations of human thinking in the evaluation process, the evaluation value of a nursing home site might be an interval grey number. Moreover, the evaluation indicator system for nursing home locations is a two-layer system that has been neglected in the literature. Therefore, the fuzzy analytical hierarchy process is extended to a new grey approach, i.e., the grey analytic hierarchy process, which can solve the evaluation problems for a two-layer indicator system under an interval grey environment. By constructing a three-point interval grey number, grey evaluation criteria are given to obtain a judgment matrix for interval grey numbers. Definitions of the initial weights, nongreyness weights and integrated weights are proposed to find the best evaluation object. Finally, the effectiveness of the method proposed by this paper is verified by comparative analyses of other grey methods.
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Ji, Xueer, Lei Wang, and Huifeng Xue. "Interval Intuitionistic Fuzzy Decision Model with Abnormal Information and Its Application in Talent Selection." Mathematical Problems in Engineering 2021 (March 30, 2021): 1–10. http://dx.doi.org/10.1155/2021/6620438.
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In some complex decision-making problems such as talent selection, experts often hesitate between multiple evaluation values during their decision making and can only give a range of information due to the fuzziness and imprecision of qualitative decision-making attributes. Interval intuitionistic fuzzy sets and their decision-making methods provide a useful tool to describe the fuzziness of decision attributes and decision experts’ hesitation. However, the abnormal information in the expert decision information has not been considered in the previous works; that is, some interval intuitionistic fuzzy numbers exceed the defined interval range. This kind of abnormal decision information often makes it difficult to obtain accurate decision results using the decision model. To avoid the abnormal information influence on decision-making results, the hesitancy degree-based interval intuitionistic fuzzy sets are employed to propose an adaptive correction method of abnormal information, which can correct the abnormal decision information without changing the decision preference of experts. The abnormal information correction method is utilized to construct a new interval intuitionistic fuzzy entropy by combining hesitancy and fuzziness. This provides a multiattribute decision-making method, including abnormal decision information. Finally, the effectiveness and superiority of the proposed method and decision-making model are evaluated using an application case study of talent selection.
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Cariani, P. A., and B. Delgutte. "Neural correlates of the pitch of complex tones. II. Pitch shift, pitch ambiguity, phase invariance, pitch circularity, rate pitch, and the dominance region for pitch." Journal of Neurophysiology 76, no. 3 (September 1, 1996): 1717–34. http://dx.doi.org/10.1152/jn.1996.76.3.1717.
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1. The neural correlates of low pitches produced by complex tones were studied by analyzing temporal discharge patterns of auditory nerve fibers in Dial-anesthetized cats. In the previous paper it was observed that, for harmonic stimuli, the most frequent interspike interval present in the population of auditory nerve fibers always corresponded to the perceived pitch (predominant interval hypothesis). The fraction of these most frequent intervals relative to the total number of intervals qualitatively corresponded to strength (salience) of the low pitches that are heard. 2. This paper addresses the neural correlates of stimuli that produce more complex patterns of pitch judgments, such as shifts in pitch and multiple pitches. Correlates of pitch shift and pitch ambiguity were investigated with the use of harmonic and inharmonic amplitude-modulated (AM) tones varying either in carrier frequency or modulation frequency. Pitches estimated from the pooled interval distributions showed shifts corresponding to "the first effect of pitch shift" (de Boer's rule) that is observed psychophysically. Pooled interval distributions in response to inharmonic stimulus segments showed multiple maxima corresponding to the multiple pitches heard by human listeners (pitch ambiguity). 3. AM and quasi-frequency-modulated tones with low carrier frequencies produce very similar patterns of pitch judgments, despite great differences in their phase spectra and waveform envelopes. Pitches estimated from pooled interval distributions were remarkably similar for the two kinds of stimuli, consistent with the psychophysically observed phase invariance of pitches produced by sets of low-frequency components. 4. Trains of clicks having uniform and alternating polarities were used to investigate the relation between pitches associated with periodicity and those associated with click rate. For unipolar click trains, where periodicity and rate coincide, physiologically estimated pitches closely follow the fundamental period. This corresponds to the pitch at the fundamental frequency (F0) that is heard. For alternating click trains, where rate and periodicity do not coincide, physiologically estimated pitches always closely followed the fundamental period. Although these pitch estimates corresponded to periodicity pitches that are heard for F0s > 150 Hz, they did not correspond to the rate pitches that are heard for F0s < 150 Hz. The predominant interval hypothesis thus failed to predict rate pitch. 5. When alternating-polarity click trains are high-pass filtered, rate pitches are strengthened and can also be heard at F0s > 150 Hz. Pitches for high-pass-filtered alternating click trains were estimated from pooled responses of fibers with characteristic frequencies (CFs) > 2 kHz. Roughly equal numbers of intervals at 1/rate and 1/F0 were found for all F0s studied, from 80 to 160 Hz, producing pitch estimates consistent with the rate pitches that are heard after high-pass filtering. The existence region for rate pitch also coincided with the presence of clear periodicities related to the click rate in pooled peristimulus time histograms. These periodicities were strongest for ensembles of fibers with CFs > 2 kHz, where there is widespread synchrony of discharges across many fibers. 6. The "dominance region for pitch" was studied with the use of two harmonic complexes consisting of harmonics 3-5 of one F0 and harmonics 6-12 of another fundamental 20% higher in frequency. When the complexes were presented individually, pitch estimates were always close to the fundamental of the complex. When the complexes were presented concurrently, pitch estimates always followed the fundamental of harmonics 3-5 for F0s of 150-480 Hz. For F0s of 125-150 Hz, pitch estimates followed one or the other fundamental, and for F0s < 125 Hz, pitch estimates followed the fundamental of harmonics 6-12. (ABSTRACT TRUNCATED)
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Levent, H., and Y. Yilmaz. "Translation, modulation and dilation systems in set-valued signal processing." Carpathian Mathematical Publications 10, no. 1 (July 3, 2018): 143–64. http://dx.doi.org/10.15330/cmp.10.1.143-164.
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In this paper, we investigate a very important function space consists of set-valued functions defined on the set of real numbers with values on the space of all compact-convex subsets of complex numbers for which the $p$th power of their norm is integrable. In general, this space is denoted by $L^{p}% (\mathbb{R},\Omega(\mathbb{C}))$ for $1\leq p<\infty$ and it has an algebraic structure named as a quasilinear space which is a generalization of a classical linear space. Further, we introduce an inner-product (set-valued inner product) on $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ and we think it is especially important to manage interval-valued data and interval-based signal processing. This also can be used in imprecise expectations. The definition of inner-product on $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ is based on Aumann integral which is ready for use integration of set-valued functions and we show that the space $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ is a Hilbert quasilinear space. Finally, we give translation, modulation and dilation operators which are three fundational set-valued operators on Hilbert quasilinear space $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$.
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Ali, Zeeshan, Tahir Mahmood, and Miin-Shen Yang. "Complex T-Spherical Fuzzy Aggregation Operators with Application to Multi-Attribute Decision Making." Symmetry 12, no. 8 (August 5, 2020): 1311. http://dx.doi.org/10.3390/sym12081311.
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In this paper, the novel approach of complex T-spherical fuzzy sets (CTSFSs) and their operational laws are explored and also verified with the help of examples. CTSFS composes the grade of truth, abstinence, and falsity with a condition that the sum of q-power of the real part (also for imaginary part) of the truth, abstinence, and falsity grades cannot be exceeded from a unit interval. Additionally, to examine the interrelationships among the complex T-spherical fuzzy numbers (CTSFNs), we propose two aggregation operators, called complex T-spherical fuzzy weighted averaging (CTSFWA) and complex T-spherical fuzzy weighted geometric (CTSFWG) operators. A multi-attribute decision making (MADM) problem is resolved based on CTSFNs by using the proposed CTSFWA and CTSFWG operators. To examine the proficiency and reliability of the explored works, we use an example to make comparisons between the proposed operators and some existing operators. Based on the comparison results, the proposed CTSFWA and CTSFWG operators are well suited in the fuzzy environment with legitimacy and prevalence by contrasting other existing operators.
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Moroz, Leonid V., Volodymyr V. Samotyy, and Oleh Y. Horyachyy. "Modified Fast Inverse Square Root and Square Root Approximation Algorithms: The Method of Switching Magic Constants." Computation 9, no. 2 (February 17, 2021): 21. http://dx.doi.org/10.3390/computation9020021.
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Many low-cost platforms that support floating-point arithmetic, such as microcontrollers and field-programmable gate arrays, do not include fast hardware or software methods for calculating the square root and/or reciprocal square root. Typically, such functions are implemented using direct lookup tables or polynomial approximations, with a subsequent application of the Newton–Raphson method. Other, more complex solutions include high-radix digit-recurrence and bipartite or multipartite table-based methods. In contrast, this article proposes a simple modification of the fast inverse square root method that has high accuracy and relatively low latency. Algorithms are given in C/C++ for single- and double-precision numbers in the IEEE 754 format for both square root and reciprocal square root functions. These are based on the switching of magic constants in the initial approximation, depending on the input interval of the normalized floating-point numbers, in order to minimize the maximum relative error on each subinterval after the first iteration—giving 13 correct bits of the result. Our experimental results show that the proposed algorithms provide a fairly good trade-off between accuracy and latency after two iterations for numbers of type float, and after three iterations for numbers of type double when using fused multiply–add instructions—giving almost complete accuracy.
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Zhou, Jian-Rong, and Yu-Qiu Zhao. "Uniform asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2096 (April 11, 2008): 2091–112. http://dx.doi.org/10.1098/rspa.2007.0385.
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The Pollaczek weight is an example of the non-Szegö class. In this paper, we investigate the asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach. In the analysis, the original endpoints ±1 of the orthogonal interval are shifted to the Mhaskar–Rakhmanov–Saff numbers α n and β n . It is also shown, by analysing the singularities of the ϕ -function, that the endpoint parametrices constructed in terms of the Airy function are bound to be local. Asymptotic approximations are obtained in overlapping regions that cover the whole complex plane. The approximations, some special values and the leading and recurrence coefficients are compared with the known results.
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Murton, Olivia, Lauryn Zipse, Nori Jacoby, and Stefanie Shattuck-Hufnagel. "Repetition and a Beat-Based Timing Framework: What Determines the Duration of Intervals Between Repetitions of a Tapping Pattern?" Timing & Time Perception 5, no. 3-4 (December 8, 2017): 244–59. http://dx.doi.org/10.1163/22134468-00002095.
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The production of speech and music are two human behaviors that involve complex hierarchical structures with implications for timing. Timing constraints may arise from a human proclivity to form ‘self-organized’ metrical structures for perceived and produced event sequences, especially those that involve repetition. To test whether the propensity to organize events in time arises even for simple motor behaviors, we developed a novel experimental tapping paradigm investigating whether participants use the beat structure of a tapped pattern to determine the interval between repetitions. Participants listened to target patterns of 3, 4, or 5 events, occurring at one of four periodic rates, and tapped out the pattern 11 times, creating 10 inter-pattern intervals (IPIs), which participants chose freely. The ratio between mean IPI and mean inter-tap interval (ITI) was used to measure the beat-relatedness of the overall timing pattern; the closer this ratio is to an integer, the more likely the participant was timing the IPI to match a multiple of the target pattern beat. Results show that a beat-based strategy contributes prominently, although not universally, to IPI duration. Moreover, participants preferred interval cycles with even numbers of beats, especially cycles with four beats. Finally, the IPI/ITI ratio was affected by rate, with more beats of silence for the IPI at faster rates. These findings support the idea that people can generate a larger global timing structure when engaging in the repetition of simple periodic motor patterns, and use that structure to govern the timing of those motor events.
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Kose, Erkan, and Jeffrey Yi-Lin Forrest. "N-person grey game." Kybernetes 44, no. 2 (February 2, 2015): 271–82. http://dx.doi.org/10.1108/k-04-2014-0073.
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Purpose – One important assumption in the conventional cooperative game theory is that payoffs are assumed to be deterministic. In terms of the players’ cognitive ability of the realistic world, this is a very strict assumption. The classical game theory can find no way out when a particular game circumstance involves uncertainty, such as limited knowledge, small sample, and inadequate information, the payoff values of the game can only be described with interval grey numbers. The paper aims to discuss these issues. Design/methodology/approach – In this study the concept of N-person grey games is proposed in which payoffs are represented with interval grey numbers opposed to the classical game theory. A straight forward solution methodology is submitted compatible to grey numbers. Then, a currency war between anonymous countries is handled and modeled as an N-Person grey game. A generic currency war scenario is developed to follow the proposed solution procedure thoroughly. Findings – Based on the outcomes of this work, the authors can say that N-person grey game is an expansion of the classical N-person game under uncertain grey information and can be applied in more complex and uncertain environments, such as those seen in complicated currency warfare. Originality/value – This study combines the grey system theory with the classic N-person game theory and sets up the N-person grey game with grey payoff functions. Based on the grey number operating methods, the grey linear programming algorithm is established to calculate and distribute benefits to the players. In this respect this study has the feature of being the pioneer in the N-person grey game area.
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Bullett, Shaun, and Marianne Freiberger. "Hecke Groups, Polynomial Maps and Matings." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 3922–31. http://dx.doi.org/10.1142/s0217979203021915.
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We show that there is a topological conjugacy between the action of the Hecke group Gn on the completed positive real axis and the action of the shift on base n-1 expressions of real numbers in the unit interval. This conjugacy is shown to occur in holomorphic dynamical systems: we construct (n-1:n-1) holomorphic correspondences (multivalued self-maps of the Riemann sphere) which are matings between Gn acting on the complex upper half plane, and polynomials of degree n-1 acting on their filled Julia sets. Certain of these correspondences split into unions of (2:2) and (1:1) correspondences: we present combinatorial descriptions of limit sets and the connectivity locus in the case n=4.
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Wang, Ming Wu, Shuai Qin, and Peng Hua. "Risk Analysis of Shrink and Expansion for Expansive Soils and Improved Expansive Soils in the Xinqiao Airport Runway of Hefei." Applied Mechanics and Materials 90-93 (September 2011): 1307–12. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.1307.
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Risk analysis of shrinking and swelling of expansive soils and improved expansive soils with lime (IESL) for airport runway projection is a complex uncertainty problem. To select the rational foundation treatment plan and ensure the safe operation of runway, herein combined with the features of expansive soils in the runway area of Xinqiao international airport of Hefei, a novel risk analysis method was proposed to classify shrinkage and swell of expansive soils and IESLs by means of coupling set pair analysis with stochastic simulation of triangular fuzzy numbers. A function of six elements connection number was introduced to depict hierarchy and fuzziness of membership between the evaluation sample and the classification standard. Moreover, triangular fuzzy numbers simulated by a stochastic simulation method were presented to specify the component coefficients of discrepancy degree. Then a risk analysis model was described to calculate reliable degree corresponding to a confidence interval. Finally, comparisons of shrinkage and swell for foundation treatment plans of different lime content were conducted. The results will provide basis for the risk design and risk management of runway project on the expansive soils.
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Milošević, Mimica R., Dušan M. Milošević, Ana D. Stanojević, Dragan M. Stević, and Dušan J. Simjanović. "Fuzzy and Interval AHP Approaches in Sustainable Management for the Architectural Heritage in Smart Cities." Mathematics 9, no. 4 (February 4, 2021): 304. http://dx.doi.org/10.3390/math9040304.
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For the past four decades, the methodology of fuzzy analytic hierarchy process based on fuzzy trapezoidal or triangular numbers with the linear type of membership functions has witnessed an expanding development with applicability to a wide variety of areas, such as industry, environment, education, government, economics, engineering, health, and smart city leadership. On the other hand, the interval gray analytic hierarchy process is a more practical method when a significant number of professionals have large variations in preferences and interests in complex decisions. The paper examines the management of architectural heritage in smart cities, using methods of multi-criteria decision making. Two appropriate methods generally recommended by the scientific literature have been applied: fuzzy and interval grey analytic hierarchy process. By using both techniques, there is an opportunity to analyze the consensual results from the aspect of two different stakeholder groups: architectural heritage experts and smart city development experts. Trapezoidal fuzzy analytical hierarchical process shows better stability than a triangular one. Both approaches assign priority to the strategy, but the interval approach gives a more significant rank to architectural heritage factors. The similarity of the proposed methods has been tested, and the similarity factor in the ranking indicates a high degree of similarity in comparing the reference rankings.
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Yan, Jiong, Katherina Walz, Hisashi Nakamura, Sandra Carattini-Rivera, Qi Zhao, Hannes Vogel, Ning Wei, Monica J. Justice, Allan Bradley, and James R. Lupski. "COP9 Signalosome Subunit 3 Is Essential for Maintenance of Cell Proliferation in the Mouse Embryonic Epiblast." Molecular and Cellular Biology 23, no. 19 (October 1, 2003): 6798–808. http://dx.doi.org/10.1128/mcb.23.19.6798-6808.2003.
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ABSTRACT Csn3 (Cops3) maps to the mouse chromosome 11 region syntenic to the common deletion interval for the Smith-Magenis syndrome, a contiguous gene deletion syndrome. It encodes the third subunit of an eight-subunit protein complex, the COP9 signalosome (CSN), which controls a wide variety of molecules of different functions. Mutants of this complex caused lethality at early development of both plants and Drosophila melanogaster. CSN function in vivo in mammals is unknown. We disrupted the murine Csn3 gene in three independent ways with insertional vectors, including constructing a ≈3-Mb inversion chromosome. The heterozygous mice appeared normal, although the protein level was reduced. Csn3−/− embryos arrested after 5.5 days postcoitum (dpc) and resorbed by 8.5 dpc. Mutant embryos form an abnormal egg cylinder which does not gastrulate. They have reduced numbers of epiblast cells, mainly due to increased cell death. In the Csn3−/− mice, subunit 8 of the COP9 complex was not detected by immunohistochemical techniques, suggesting that the absence of Csn3 may disrupt the entire COP9 complex. Therefore, Csn3 is important for maintaining the integrity of the COP9 signalosome and is crucial to maintain the survival of epiblast cells and thus the development of the postimplantation embryo in mice.
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Gligoric, Zoran, Lazar Kricak, Cedomir Beljic, Suzana Lutovac, and Jelena Milojevic. "Evaluation of Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian Motion." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/914643.
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Underground mine projects are often associated with diverse sources of uncertainties. Having the ability to plan for these uncertainties plays a key role in the process of project evaluation and is increasingly recognized as critical to mining project success. To make the best decision, based on the information available, it is necessary to develop an adequate model incorporating the uncertainty of the input parameters. The model is developed on the basis of full discounted cash flow analysis of an underground zinc mine project. The relationships between input variables and economic outcomes are complex and often nonlinear. Fuzzy-interval grey system theory is used to forecast zinc metal prices while geometric Brownian motion is used to forecast operating costs over the time frame of the project. To quantify the uncertainty in the parameters within a project, such as capital investment, ore grade, mill recovery, metal content of concentrate, and discount rate, we have applied the concept of interval numbers. The final decision related to project acceptance is based on the net present value of the cash flows generated by the simulation over the time project horizon.
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Shi, Lilian, and Yue Yuan. "Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM." Symmetry 11, no. 2 (February 21, 2019): 278. http://dx.doi.org/10.3390/sym11020278.
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Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.
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Luo, Dang, and Zhang Huihui. "Grey clustering model based on kernel and information field." Grey Systems: Theory and Application 10, no. 1 (November 1, 2019): 56–67. http://dx.doi.org/10.1108/gs-08-2019-0029.
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Purpose The purpose of this paper is to propose a grey clustering model based on kernel and information field to deal with the situation in which both the observation values and the turning points of the whitenization weight function are interval grey numbers. Design/methodology/approach First, the “unreduced axiom of degree of greyness” was expanded to obtain the inference of “information field not-reducing”. Then, based on the theoretical basis of inference, the expression of whitenization weight function with interval grey number was provided. The grey clustering model and fuzzy clustering model were compared to analyse the relationship and difference between the two models. Finally, the paper model and the fuzzy clustering model were applied to the example analysis, and the interval grey number clustering model was established to analyse the influencing factors of regional drought disaster risk in Henan Province. Findings The example analysis results illustrate that although the two clustering methods have different theoretical basis, they are suitable for dealing with complex systems with uncertainty or grey characteristic, solving the problem of incomplete system information, which has certain feasibility and rationality. The clustering results of case study show that five influencing factors of regional drought disaster risk in Henan Province are divided into three classes, consistent with the actual situation, and they show the validity and practicability of the clustering model. Originality/value The paper proposes a new whitenization weight function with interval grey number that can transform interval grey number operations into real number operations. It not only simplifies the calculation steps, but it has a great significance for the “small data sets and poor information” grey system and has a universal applicability.
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Wang, Dazhi, and Yang Chen. "Study on permanent magnetic drive forecasting by designing Takagi Sugeno Kang type interval type-2 fuzzy logic systems." Transactions of the Institute of Measurement and Control 40, no. 6 (March 28, 2018): 2011–23. http://dx.doi.org/10.1177/0142331217694682.
Full textAbstract:
The process of permanent magnetic drive (PMD) presents high uncertainty under the complex operating conditions. In this paper, a type of Takagi Sugeno Kang (TSK) interval type-2 fuzzy logic systems (IT2 FLSs) under the Karnik-Mendel (KM) structure is designed for data-based PMD torque and revolutions per minute (rpm) forecasting. For designing the antecedent and input measurement of TSK IT2 FLSs, the primary membership functions (MFs) of interval type-2 fuzzy sets (IT2 FSs) are all selected as Gaussian type-2 MFs with uncertain derivation, while the consequent parameters are chosen as type-1 fuzzy numbers. According to matrix transformation, the complicated task of calculating derivatives in the TSK IT2 FLSs under the Karnik-Mendel structure can be managed subtly by some elementary vectors and partitioned matrices. And the parameters of the proposed systems are also tuned by the back propagation (BP) algorithms. Simulation examples based on the data of PMD torque and rpm are used to test the advanced fuzzy logic systems forecasting methods. The effective and feasibility of forecasting by the proposed type-2 systems compared with their type-1 counterparts is illustrated in the light of Monte Carlo simulations, convergence and stability analysis.