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1

Ragin, Charles C., and Paul Pennings. "Fuzzy Sets and Social Research." Sociological Methods & Research 33, no. 4 (May 2005): 423–30. http://dx.doi.org/10.1177/0049124105274499.

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2

Herrera, F., and J. L. Verdegay. "Fuzzy sets and operations research: Perspectives." Fuzzy Sets and Systems 90, no. 2 (September 1997): 207–18. http://dx.doi.org/10.1016/s0165-0114(97)00088-2.

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3

Lin, Robert. "Note on fuzzy sets." Yugoslav Journal of Operations Research 24, no. 2 (2014): 299–303. http://dx.doi.org/10.2298/yjor130202010l.

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We present some improvements for the landmark paper of fuzzy sets for distributive law, convex combination and convex fuzzy sets. Our enhancement will help researcher absorb the original paper of fuzzy sets.
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4

Atanassov, Krassimir T. "Research on intuitionistic fuzzy sets, 1990–1992." Fuzzy Sets and Systems 54, no. 3 (March 1993): 363–64. http://dx.doi.org/10.1016/0165-0114(93)90390-4.

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5

Atanassov, Krassimir T. "Research on intuitionistic fuzzy sets in Bulgaria." Fuzzy Sets and Systems 22, no. 1-2 (April 1987): 193. http://dx.doi.org/10.1016/0165-0114(87)90019-4.

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6

Angelova, Nora, and Krassimir Atanassov. "Research on intuitionistic fuzzy implications." Notes on Intuitionistic Fuzzy Sets 27, no. 2 (August 2021): 20–93. http://dx.doi.org/10.7546/nifs.2021.27.2.20-93.

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7

Wu, Xinlin, and Yong Zhao. "Research on Bounded Rationality of Fuzzy Choice Functions." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/928279.

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The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function, and especially the fuzzy choice function with bounded rationality is studied combined with some rationality conditions. Results show that the fuzzy choice function with bounded rationality also satisfies some important rationality conditions, but not vice versa. The research gives supplements to the investigation in the framework of the Banerjee choice function.
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8

Liu, Yong Shan, and Yan Li. "Analysis and Research of Direction Relation Based on Fuzzy Description." Advanced Materials Research 393-395 (November 2011): 1102–5. http://dx.doi.org/10.4028/www.scientific.net/amr.393-395.1102.

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A fuzzy membership function was defined for each direction to predict the membership degree that an object pertains to a certain direction. Nine fuzzy membership functions were defined to describe the direction relations between fuzzy objects and crisp objects with corresponding fuzzy sets. Direction relations were described by a 3×3 fuzzy matrix, which was computed by an aggregation operator defined on the nine fuzzy sets. The fuzzy matrices and crisp matrices of direction relations between fuzzy objects and crisp objects were computed respectively, and comparison of fuzzy matrices with crisp ones reveals that the proposed fuzzy approach is more effective than existing crisp method.
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9

Wang, Jing, and Gao Zheng. "An Inclusion Measure between Fuzzy Sets." Applied Mechanics and Materials 740 (March 2015): 769–72. http://dx.doi.org/10.4028/www.scientific.net/amm.740.769.

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The inclusion measure is an important index of fuzzy logic because of its wide application. This paper aims to put forward a new fuzzy inclusion measure. Based on the previous related research results, an axiomatic definition with three axioms is first chosen for the purpose of making the fuzzy inclusion measure in the true spirit of fuzzy logic. A calculation formula is built under the constraints of the chosen definition, that is to say that the calculation formula is consistent with the three axioms. Two properties are discussed. Finally, two examples are used to verify the rationality of the new inclusion measure between fuzzy sets.
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10

Li, Qiao Yan, Yan Yan Chen, and Shao Yang Li. "Research on the N-Reduction of Fuzzy Covering Rough Sets." Applied Mechanics and Materials 556-562 (May 2014): 3682–85. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3682.

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The granular reduction plays an important role in covering rough sets, and the aim of this paper is to explore the granular reduction of covering rough sets and fuzzy covering rough set Firstly, the covering rough sets based on neighborhood element and the N-reduction are introduced, and their properties are discussed; secondly, The definitions and properties of upper and lower approximation of fuzzy covering rough based on the neighborhood are given; Lastly, the N- reduction of fuzzy covering rough based on the neighborhood element is proposed, and we can get that covering rough sets remain the same upper and lower approximations for N-reduction.
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11

Verdegay, Jose L. "Fuzzy Sets in Decision Analysis, Operations Research and Statistics." Fuzzy Sets and Systems 123, no. 3 (November 2001): 407–9. http://dx.doi.org/10.1016/s0165-0114(01)00095-1.

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12

Shu-min, Li. "Fuzzy sets and linguistics research at NPU, Xi'an, China." Fuzzy Sets and Systems 32, no. 1 (August 1989): 131. http://dx.doi.org/10.1016/0165-0114(89)90098-5.

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13

徐, 伟华. "The Research of Several Propositions on Starshaped Fuzzy Sets." Operations Research and Fuzziology 01, no. 01 (2011): 6–10. http://dx.doi.org/10.12677/orf.2011.11002.

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14

Vij, Sonakshi, Amita Jain, Devendra Tayal, and Oscar Castillo. "Scientometric inspection of research progression in hesitant fuzzy sets." Journal of Intelligent & Fuzzy Systems 38, no. 1 (January 9, 2020): 619–26. http://dx.doi.org/10.3233/jifs-179435.

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15

Kaufmann, A. "On the relevance of fuzzy sets for operations research." European Journal of Operational Research 25, no. 3 (January 1986): 330–35. http://dx.doi.org/10.1016/0377-2217(86)90264-x.

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16

Driankov, D. "Fuzzy sets and many-valued logic research in Sweden." Fuzzy Sets and Systems 24, no. 1 (October 1987): 135–37. http://dx.doi.org/10.1016/0165-0114(87)90125-4.

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17

Mayne, Alan J., George J. Klir, and Tina A. Folger. "Fuzzy Sets, Uncertainty, and Information." Journal of the Operational Research Society 41, no. 9 (September 1990): 884. http://dx.doi.org/10.2307/2583508.

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18

Mayne, Alan J. "Fuzzy Sets, Uncertainty, and Information." Journal of the Operational Research Society 41, no. 9 (September 1990): 884–86. http://dx.doi.org/10.1057/jors.1990.130.

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19

Dubois, Didier, and Henri Prade. "Fuzzy sets and statistical data." European Journal of Operational Research 25, no. 3 (January 1986): 345–56. http://dx.doi.org/10.1016/0377-2217(86)90266-3.

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20

Dubois, Didier, and Henri Prade. "Fuzzy sets, probability and measurement." European Journal of Operational Research 40, no. 2 (May 1989): 135–54. http://dx.doi.org/10.1016/0377-2217(89)90326-3.

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21

Joshi, Bhagawati P., and Sanjay Kumar. "Fuzzy Time Series Model Based on Intuitionistic Fuzzy Sets for Empirical Research in Stock Market." International Journal of Applied Evolutionary Computation 3, no. 4 (October 2012): 71–84. http://dx.doi.org/10.4018/jaec.2012100105.

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Intuitionistic fuzzy sets introduced by Atanassov are generalization of fuzzy sets as they also handle the non-determinacy which is caused by degree of hesitation of decision maker. The present study proposes a computational method of forecasting for fuzzy time series. In the proposed method the notion of intuitionistic fuzzy set is used in fuzzy time series forecasting with simplified computational approach. The developed model has been tested on the movement of share market prices of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. Further the method has been implemented for forecasting SENSEX of BSE. The suitability of the developed model has also been examined by comparing it with the other existing models to show its superiority.
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22

Atanassov, Krassimir, and Evgeniy Marinov. "Four Distances for Circular Intuitionistic Fuzzy Sets." Mathematics 9, no. 10 (May 15, 2021): 1121. http://dx.doi.org/10.3390/math9101121.

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In the paper, for the first time, four distances for Circular Intuitionistic Fuzzy Sets (C-IFSs) are defined. These sets are extensions of the standard IFS that are extensions of Zadeh’s fuzzy sets. As it is shown, the distances for the C-IFS are different than those for the standard IFSs. At the moment, they do not have analogues in fuzzy sets theory. Examples, comparing the proposed distances, are given and some ideas for further research are formulated.
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23

Tang, Weidong, Jinzhao Wu, and Dingwei Zheng. "On Fuzzy Rough Sets and Their Topological Structures." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/546372.

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The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper is devoted to the discussion of fuzzy rough sets and their topological structures. Fuzzy rough approximations are further investigated. Fuzzy relations are researched by means of topology or lower and upper sets. Topological structures of fuzzy approximation spaces are given by means of pseudoconstant fuzzy relations. Fuzzy topology satisfying (CC) axiom is investigated. The fact that there exists a one-to-one correspondence between the set of all preorder fuzzy relations and the set of all fuzzy topologies satisfying (CC) axiom is proved, the concept of fuzzy approximating spaces is introduced, and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained, which illustrates that we can research fuzzy relations or fuzzy approximation spaces by means of topology and vice versa. Moreover, fuzzy pseudoclosure operators are examined.
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24

GLUSHKOVSKY, ELI A., and RADU A. FLORESCU. "FUZZY SETS APPROACH TO QUALITY IMPROVEMENT." Quality and Reliability Engineering International 12, no. 1 (January 1996): 27–37. http://dx.doi.org/10.1002/(sici)1099-1638(199601)12:1<27::aid-qre978>3.0.co;2-v.

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25

Ovchinnikov, Sergei V. "Survey of research on fuzzy sets in the Soviet Union." Journal of Statistical Planning and Inference 20, no. 3 (January 1988): 413–28. http://dx.doi.org/10.1016/0378-3758(88)90100-0.

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26

Drossos, Costas. "Research on fuzzy sets and nonstandard mathematics in Patras, Greece." Fuzzy Sets and Systems 40, no. 1 (March 1991): 245–47. http://dx.doi.org/10.1016/0165-0114(91)90053-s.

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27

Wang, Lei, Mingfang Ni, and Lei Zhu. "Correlation Measures of Dual Hesitant Fuzzy Sets." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/593739.

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The dual hesitant fuzzy sets (DHFSs) were proposed by Zhu et al. (2012), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Correlation measures analysis is an important research topic. In this paper, we define the correlation measures for dual hesitant fuzzy information and then discuss their properties in detail. One numerical example is provided to illustrate these correlation measures. Then we present a direct transfer algorithm with respect to the problem of complex operation of matrix synthesis when reconstructing an equivalent correlation matrix for clustering DHFSs. Furthermore, we prove that the direct transfer algorithm is equivalent to transfer closure algorithm, but its asymptotic time complexity and space complexity are superior to the latter. Another real world example, that is, diamond evaluation and classification, is employed to show the effectiveness of the association coefficient and the algorithm for clustering DHFSs.
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28

Wang, Lu, and Keyun Qin. "Incomplete Fuzzy Soft Sets and Their Application to Decision-Making." Symmetry 11, no. 4 (April 13, 2019): 535. http://dx.doi.org/10.3390/sym11040535.

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The research of incomplete fuzzy soft sets is of paramount importance in fuzzy soft sets, where the combination of incomplete fuzzy soft set and decision-making problem is of great significance. Incomplete information in fuzzy soft sets leads to more uncertainty and ambiguity in decision-making. The focus of this paper to propose an algorithm of fuzzy soft set based decision-making problems under incomplete information. On the basis of the weighted function, we introduce the notions of weighted incomplete soft sets and weighted incomplete fuzzy soft sets, and show an approach to weighted incomplete fuzzy soft sets for dealing with decision-making. Considering the missing weight function, the concept of incomplete weighted fuzzy soft sets is presented. Meanwhile, we apply the incomplete weighted fuzzy soft sets to solve the decision-making problem. As modal-style operators for fuzzy soft sets have a precise description of attributes possessed by objects, we apply modal-style operator for incomplete fuzzy soft set to deal with decision-making and propose a new algorithm to make it more accurate and simple.
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29

Yiyan, Chen, Li Ye, and Li Cunjin. "Research on the multiple fuzzy parametric fuzzy sets and its framework of clustering algorithm." Evolutionary Intelligence 13, no. 2 (February 28, 2020): 159–83. http://dx.doi.org/10.1007/s12065-020-00354-3.

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30

Simanihuruk, Tiarma, H. Hartono, Dahlan Abdullah, Cut Ita Erliana, Darmawan Napitupulu, Erianto Ongko, Robbi Rahim, Sukiman ., and Ansari Saleh Ahmar. "Hesitant Fuzzy Linguistic Term Sets with Fuzzy Grid Partition in Determining the Best Lecturer." International Journal of Engineering & Technology 7, no. 2.3 (March 8, 2018): 59. http://dx.doi.org/10.14419/ijet.v7i2.3.12322.

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Decision-making on conditions that involve many alternatives, many criteria, and many judgments is a difficult thing to do. The difficulty is coupled with assessors who sometimes make decisions in hesitant, unclear, and inconsistent circumstances and each person can provide different judgments. One of the methods that can be used is Hesitant Fuzzy Linguistic Term Sets which is the development of Fuzzy Sets that can make decisions by using Hesitant Fuzzy Sets. Hesitant linguistic term has been introduced for capturing the human way of reasoning using linguistic expressions involving different levels of precision. The integration of Hesitant Fuzzy Linguistic Term Sets with Fuzzy Grid Partition will enhance the ability in the decision making process. This research will discuss the use of Hesitant Fuzzy Linguistic Term Sets method and Fuzzy Grid Partition for best lecturers determination.
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31

Kamali, Anahid, and Hamid Reza Moradi. "Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces." International Journal of Fuzzy System Applications 5, no. 2 (April 2016): 1–12. http://dx.doi.org/10.4018/ijfsa.2016040101.

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The purpose of this research article is to explain the meaning of g-closed sets in fuzzy topological spaces, which is more understandable to the readers and we find some of its basic properties. The concept of fuzzy sets was introduced by Zadeh in his classical paper (1965). Thereafter many investigations have been carried out, in the general theoretical field and also in different applied areas, based on this concept. The idea of fuzzy topological space was introduced by Chang (1968). The idea is more or less a generalization of ordinary topological spaces. Different aspects of such spaces have been developed, by several investigators. This paper is also devoted to the development of the theory of fuzzy topological spaces.
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32

Zahran, A. M., and A. I. El-Maghrabi. "Generalizedψρ-Operations on Fuzzy Topological Spaces." Abstract and Applied Analysis 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/164510.

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The aim of this work is to introduceψ-operations on fuzzy topological spaces and to use them to study fuzzy generalizedψρ-closed sets and fuzzy generalizedψρ-open sets. Also, we introduce some characterizations and properties for these concepts. Finally we show that certain results of several publications on the concepts of weakness and strength of fuzzy generalized closed sets are considered as corollaries of the results of this research.
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33

Liu, Yaya, Keyun Qin, Chang Rao, and Mahamuda Alhaji Mahamadu. "Object–Parameter Approaches to Predicting Unknown Data in an Incomplete Fuzzy Soft Set." International Journal of Applied Mathematics and Computer Science 27, no. 1 (March 28, 2017): 157–67. http://dx.doi.org/10.1515/amcs-2017-0011.

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Abstract The research on incomplete fuzzy soft sets is an integral part of the research on fuzzy soft sets and has been initiated recently. In this work, we first point out that an existing approach to predicting unknown data in an incomplete fuzzy soft set suffers from some limitations and then we propose an improved method. The hidden information between both objects and parameters revealed in our approach is more comprehensive. Furthermore, based on the similarity measures of fuzzy sets, a new adjustable object-parameter approach is proposed to predict unknown data in incomplete fuzzy soft sets. Data predicting converts an incomplete fuzzy soft set into a complete one, which makes the fuzzy soft set applicable not only to decision making but also to other areas. The compared results elaborated through rate exchange data sets illustrate that both our improved approach and the new adjustable object-parameter one outperform the existing method with respect to forecasting accuracy.
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34

Kumar, Sanjay, and Sukhdev Singh Gangwar. "A fuzzy time series forecasting method induced by intuitionistic fuzzy sets." International Journal of Modeling, Simulation, and Scientific Computing 06, no. 04 (December 2015): 1550041. http://dx.doi.org/10.1142/s1793962315500415.

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Intuitionistic fuzzy sets (IFSs) are well established as a tool to handle the hesitation in the decision system. In this research paper, fuzzy sets induced by IFS are used to develop a fuzzy time series forecasting model to incorporate degree of hesitation (nondeterminacy). To improve the forecasting accuracy, induced fuzzy sets are used to establish fuzzy logical relations. To verify the performance of the proposed model, it is implemented on one of the benchmarking time series data. Further, developed forecasting method is also tested and validated by applying it on a financial time series data. In order to show the accuracy in forecasting, the method is compared with other forecasting methods using different error measures.
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35

Rohlfing, Ingo. "The Choice between Crisp and Fuzzy Sets in Qualitative Comparative Analysis and the Ambiguous Consequences for Finding Consistent Set Relations." Field Methods 32, no. 1 (December 27, 2019): 75–88. http://dx.doi.org/10.1177/1525822x19896258.

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Empirical researchers using qualitative comparative analysis (QCA) can work with crisp, multivalue, and fuzzy sets. The relative advantages of crisp and multivalue sets have been discussed in the QCA literature. There has been little reflection on the more frequent decision between crisp and fuzzy sets for which there often is no theoretical guidance. A review shows that researchers often prefer fuzzy over crisp sets, sometimes because they contain more information. This meets with the argument that fuzzy sets produce more conservative consistency measures and constitute tougher tests. In my article, I demonstrate analytically and with data from published QCA studies that the relationship between crisp sets, fuzzy sets, and the consistency score is ambiguous. It depends on the distribution of cases whether the consistency value is more or less conservative for fuzzy sets than for crisp sets. I outline the implications of the ambiguous relationship for empirical research.
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36

Yang, Qing Bo, and Jian Long Zhou. "Generalized Set Theories Applied in Uncertain Information Processing." Applied Mechanics and Materials 644-650 (September 2014): 2419–23. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.2419.

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Uncertain factors in information bring us serious challenges. In order to apply information effectively, many researchers are committed to the research on uncertain information processing. Generalized set theories are widely used in the research. Several kinds of theories such as Fuzzy sets, Intuitionistic fuzzy sets, Vague sets, Rough sets and Extension sets are introduced in this paper. And a comparation and analysis of them is given in the following.
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37

Osadchyi, V. V., V. S. Yeremeev, A. V. Matsyura, and K. Jankowski. "Cluster analysis, fuzzy sets, and fuzzy logic models in bird identification." Ukrainian Journal of Ecology 7, no. 2 (May 22, 2017): 96–103. http://dx.doi.org/10.15421/2017_25.

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<p>In our resent research (Osadchiy at al., 2016) we considered the mathematical model for the identifying of bird species according to the results of inaccurate field measurements. We used the total length of the bird, the wingspan, the wingbeat frequency, and the flight as the input factors of the model. Testing the model on a hypothetical case of identifying some target species, like Rook, Common raven, Mallard, White Stork, and Lapwing revealed that this model can be used for bird species identification with definite limitations. However, in previous model we applied the recognition algorithm that was based on the classical sections of mathematical statistics. The limitations of those model are obvious - it does not take into account many characteristics and behavioral features of birds that cannot be represented in numerical form, like diurnal activity pattern and flocking behavior. In this case the possibility of using the traditional sections of mathematical statistics is quite limited. The present study is devoted to the development of a mathematical method for the identifying of the bird species that based on cluster analysis with fuzzy logic and fuzzy sets which extends the possibilities of the algorithm that was previously proposed in our research.</p>
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38

Wang, Jian Qiang, Dan Dan Wang, Hong yu Zhang, and Xiao Hong Chen. "Multi-criteria outranking approach with hesitant fuzzy sets." OR Spectrum 36, no. 4 (November 7, 2013): 1001–19. http://dx.doi.org/10.1007/s00291-013-0354-3.

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39

Niewiadomski, A., and M. Kacprowicz. "Higher order fuzzy logic in controlling selective catalytic reduction systems." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 4 (December 1, 2014): 743–50. http://dx.doi.org/10.2478/bpasts-2014-0080.

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Abstract This paper presents research on applications of fuzzy logic and higher-order fuzzy logic systems to control filters reducing air pollution [1]. The filters use Selective Catalytic Reduction (SCR) method and, as for now, this process is controlled manually by a human expert. The goal of the research is to control an SCR system responsible for emission of nitrogen oxide (NO) and nitrogen dioxide (NO2) to the air, using SCR with ammonia (NH3). There are two higher-order fuzzy logic systems presented, applying interval-valued fuzzy sets and type-2 fuzzy sets, respectively. Fuzzy sets and higher order fuzzy sets describe linguistically levels of nitrogen oxides as the input, and settings of ammonia valve in the air filter as the output. The obtained results are consistent with data provided by experts. Besides, we show that the type-2 fuzzy logic controllers allows us to obtain results much closer to desired parameters of the ammonia valve, than traditional FLS.
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40

Janková, Zuzana, and Petr Dostál. "Type-2 Fuzzy Expert System Approach for Decision-Making of Financial Assets and Investing under Different Uncertainty." Mathematical Problems in Engineering 2021 (June 18, 2021): 1–16. http://dx.doi.org/10.1155/2021/3839071.

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Extensive research results of stock market time series using classical fuzzy sets (type-1) are available in the literature. However, type-1 fuzzy sets cannot fully capture the uncertainty associated with stock market developments due to their limited descriptiveness. This paper fills a scientific gap and focuses on type-2 fuzzy logic applied to stock markets. Type-2 fuzzy sets may include additional uncertainty resulting from unclear, uncertain, or inaccurate financial data through which model inputs are calculated. Here we propose four methods based on type-2 fuzzy logic, which differ in the level of uncertainty contained in fuzzy sets and compared with the type-1 fuzzy model. The case study aims to create a model to support investment decisions in Exchange-Traded Funds (ETFs) listed on international equity markets. The created models of type-2 fuzzy logic are compared with the classic type-1 fuzzy logic model. Based on the results of the comparison, it can be said that type-2 fuzzy logic with dual fuzzy sets is able to better describe data from financial time series and provides more accurate outputs. The results reflect the capability and effectiveness of the approach proposed in this document. However, the performance of type-2 fuzzy logic models decreases with the inclusion of increasing uncertainty in fuzzy sets. For further research, it would be appropriate to examine the different levels of uncertainty in the input parameters themselves and monitor the performance of such a modified model.
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41

Hao, Jing, Yong Xiang Zhang, Qi Jing, and Guo Feng Ning. "Research on Groundwater Quality Evaluation with Fuzzy Mathematics." Advanced Materials Research 347-353 (October 2011): 2287–94. http://dx.doi.org/10.4028/www.scientific.net/amr.347-353.2287.

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Given the ambiguity of the type and classification in groundwater quality standards, this paper based on fuzzy mathematics theory, take TDS, fluoride and other components as the nine evaluation factors, determine its weight according to the pollution of different factors on water quality; using fuzzy membership to describe the classification boundaries of the evaluation in water quality. Established a number of pollution assessment factors of fuzzy sets such as evaluation set, membership function and weight set;after the compound operation of fuzzy matrixes, using the maximum membership degree law, to evaluate the groundwater quality of a monitoring well in study area ,the conclusions are objective.
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42

Zuo, Hong Yan, Zhou Quan Luo, and Chao Wu. "Research on Classification Effectiveness of the Novel Mamdani Fuzzy Classifier." Applied Mechanics and Materials 511-512 (February 2014): 871–74. http://dx.doi.org/10.4028/www.scientific.net/amm.511-512.871.

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A novel Mamdani fuzzy classifier based on improved chaos immune algorithm is developed, in which bilateral Gaussian membership function parameters are set as constraint conditions and the indexes of fuzzy classification effectiveness and number of correct samples of fuzzy classification as the subgoal of fitness function. Moreover, Iris database is used for classification effectiveness simulation experiment. The results show that Mamdani fuzzy classifier based on improved chaos immune algorithm can effectively improve the prediction accuracy of classification of data sets with noises and outliers.
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43

Li, Fachao, and Shuo Liu. "Research on Level Effect-Based Fuzzy Prediction Method." Applied Mechanics and Materials 519-520 (February 2014): 780–83. http://dx.doi.org/10.4028/www.scientific.net/amm.519-520.780.

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As there are many prediction problems under fuzzy environments, describing the prediction results systematically and constructing a fuzzy prediction method with good structural characteristics have attracted an extensive attention. For the prediction of investment return under fuzzy environment, we first make an analysis of general fuzzy decision-making problem, and point out its limitations. Then, we discuss the association feature between decision and membership state, and give a level effect function which can describe the recognized degree under different level cut sets. Furthermore, we establish a measure model for fuzzy optimal value based on level effect function. Finally, we apply the established model to a concrete investment example, and analyze its effectiveness in fuzzy prediction. Theoretical analysis and case study show that this method has good structural characteristics and practical significance, it can enrich the existing fuzzy prediction methods to a certain degree.
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44

Wang, Qihui, Yuhuai Wang, Huixi Zhang, and Yaping Sun. "Load Forecasting Research of Power System Based on Fuzzy Sets Algorithm." International Journal of Signal Processing, Image Processing and Pattern Recognition 9, no. 6 (June 30, 2016): 283–92. http://dx.doi.org/10.14257/ijsip.2016.9.6.25.

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45

Otto, Kevin N., and Robert N. Noyce. "Research on application of fuzzy sets to design and manufacturing integration." Fuzzy Sets and Systems 82, no. 1 (August 1996): 127–28. http://dx.doi.org/10.1016/0165-0114(96)87706-2.

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46

Ali, Ghous, G. Muhiuddin, Arooj Adeel, and Muhammad Zain Ul Abidin. "Ranking Effectiveness of COVID-19 Tests Using Fuzzy Bipolar Soft Expert Sets." Mathematical Problems in Engineering 2021 (July 24, 2021): 1–19. http://dx.doi.org/10.1155/2021/5874216.

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The theory of fuzzy bipolar soft sets is an efficient extension of soft sets for depicting the bipolarity of uncertain fuzzy soft information; however, it is limited to a single expert. The present research article introduces the theory of an innovative hybrid model called the fuzzy bipolar soft expert sets, as a natural extension of two existing models (including fuzzy soft expert sets and fuzzy bipolar soft sets). The proposed model is highly suitable for describing the bipolarity of fuzzy soft information having multiple expert opinions. Some fundamental properties of the developed hybrid model are discussed, including subset, complement, union, intersection, AND operation, and OR operation. The proposed concepts are explained with detailed examples. Moreover, to demonstrate the applicability of our initiated model, an application of the proposed hybrid model is presented along with the developed algorithm to tackle the real-world group decision-making situation, that is, ranking effectiveness of tests in spread analysis of COVID-19. Finally, a comparative analysis of the developed model with some existing mathematical tools such as fuzzy soft expert sets and fuzzy bipolar soft sets is provided to show the cogency and reliability of the initiated model.
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47

Tarrazo, Manuel, and Luis Gutierrez. "Economic expectations, fuzzy sets and financial planning." European Journal of Operational Research 126, no. 1 (October 2000): 89–105. http://dx.doi.org/10.1016/s0377-2217(99)00283-0.

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48

Kacprzyk, J. "Fuzzy sets, decision making, and expert systems." European Journal of Operational Research 38, no. 1 (January 1989): 125. http://dx.doi.org/10.1016/0377-2217(89)90482-7.

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49

Pedrycz, W. "Statistically grounded logic operators in fuzzy sets." European Journal of Operational Research 193, no. 2 (March 2009): 520–29. http://dx.doi.org/10.1016/j.ejor.2007.12.009.

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50

Tarmizi, Mahfuz, and Saman Abdurrahman. "GRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 13, no. 1 (September 26, 2019): 1. http://dx.doi.org/10.20527/epsilon.v13i1.1240.

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A Quotient group is a set which contains coset members and satisfies group definition. These cosets are formed by group and its normal subgroup. A set which contains fuzzy coset members is also called a quotient group. These fuzzy cosets are formed by a group and its fuzzy normal subgroup. The purpose of this research is to explain quotient groups induced by fuzzy normal subgroups and isomorphic between them. This research construct sets which contain fuzzy coset members, define an operation between fuzzy cosets and prove these sets under an operation between fuzzy coset satisfy group definition, and prove theorems relating to qoutient groups and homomorphism. The results of this research are is a qoutient group induced by a fuzzy normal subgroup, where is a fuzzy normal subgroup of a group , is a fuzzy coset, and the binary operation is “” where for every . An epimorphism from a group to a group and a fuzzy normal subgroup of which is constant on cause quotient goup and are isomorphic.
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