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Journal articles on the topic 'The method of pairwise comparisons'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

Zhang, Hongjun, Chengxiang Yin, Xiuli Qi, Rui Zhang, and Xingdang Kang. "Cognitive Best Worst Method for Multiattribute Decision-Making." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/1092925.

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Pairwise comparison based multiattribute decision-making (MADM) methods are widely used and studied in recent years. However, the perception and cognition towards the semantic representation for the linguistic rating scale and the way in which the pairwise comparisons are executed are still open to discuss. The commonly used ratio scale is likely to produce misapplications and the matrix based comparison style needs too many comparisons and is not able to guarantee the consistency of the matrix when the number of objects involved is large. This research proposes a new MADM method CBWM (Cogniti

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SHAMS, FARHAD, SHERIF MOHAMED, and AMINAH ROBINSON FAYEK. "IMPROVING CONSISTENCY EVALUATION IN FUZZY MULTI-ATTRIBUTE PAIRWISE COMPARISON-BASED DECISION-MAKING METHODS." Asia-Pacific Journal of Operational Research 31, no. 04 (2014): 1450024. http://dx.doi.org/10.1142/s0217595914500249.

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A typical approach to handle the complexity of multi-faceted decision-making problems is to use multi-attribute decision-making (MADM) methods based on pairwise comparisons. Fuzzy set theory has also been employed to cope with the uncertainty and vagueness involved in conducting the comparisons between components of a decision model. An important issue regarding the reliability of the output is the consistency of pairwise comparisons provided by the decision maker(s). Using the MADM method developed by Lu et al. (2007) as a foundation, this paper proposes an algorithm for evaluating the consis

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Agus Ristono, Tri Wahyuningsih, and Eko Junianto. "Proposed Method for Supplier Selection." Technium Social Sciences Journal 13 (November 3, 2020): 376–94. http://dx.doi.org/10.47577/tssj.v13i1.1955.

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The use of the Analytical Hierarchy Process (AHP) is frequent in supplier selection. First, AHP is a pairwise comparison between criteria. If the pairwise comparisons are inconsistent, the result is invalid. Thus, the process of comparing criteria must be repeated continuously until valid results are obtained. This process takes time and costs so it is considered inefficient. This research proposes the application of the Hamilton chain process into the pairwise comparison matrix. One criterion is symbolized as a knot, while the arc is symbolized as the pairwise comparison value between the two

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Benítez, Julio, Waldemar W. Koczkodaj, and Adam Kowalczyk. "Computationally efficient orthogonalization for pairwise comparisons method." Applied Mathematics and Computation 473 (July 2024): 128651. http://dx.doi.org/10.1016/j.amc.2024.128651.

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Domonkos, Peter. "Combination of Using Pairwise Comparisons and Composite Reference Series: A New Approach in the Homogenization of Climatic Time Series with ACMANT." Atmosphere 12, no. 9 (2021): 1134. http://dx.doi.org/10.3390/atmos12091134.

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The removal of non-climatic biases, so-called inhomogeneities, from long climatic records needs sophistically developed statistical methods. One principle is that the differences between a candidate series and its neighbor series are usually analyzed instead of the candidate series directly, in order to neutralize the possible impacts of regionally common natural climate variation on the detection of inhomogeneities. In most homogenization methods, two main kinds of time series comparisons are applied, i.e., composite reference series or pairwise comparisons. In composite reference series, the

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Crompvoets, Elise A. V., Anton A. Béguin, and Klaas Sijtsma. "Adaptive Pairwise Comparison for Educational Measurement." Journal of Educational and Behavioral Statistics 45, no. 3 (2019): 316–38. http://dx.doi.org/10.3102/1076998619890589.

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Pairwise comparison is becoming increasingly popular as a holistic measurement method in education. Unfortunately, many comparisons are required for reliable measurement. To reduce the number of required comparisons, we developed an adaptive selection algorithm (ASA) that selects the most informative comparisons while taking the uncertainty of the object parameters into account. The results of the simulation study showed that, given the number of comparisons, the ASA resulted in smaller standard errors of object parameter estimates than a random selection algorithm that served as a benchmark.

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Kiselev, I. S. "Analytical method for making definite multiple preferences in thematrix of incomplete pairwise comparisons." Prikladnaya diskretnaya matematika, no. 13 (September 1, 2011): 122–28. http://dx.doi.org/10.17223/20710410/13/10.

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Mazurek, Jiří, Radomír Perzina, Jaroslav Ramík, and David Bartl. "A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method." Mathematics 9, no. 5 (2021): 554. http://dx.doi.org/10.3390/math9050554.

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In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more s

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Ungvári, Edina, and István Gábor Gyurika. "Evaluation of PC-FMEA Using Network Analysis." Hungarian Journal of Industry and Chemistry 50, no. 2 (2022): 61–64. http://dx.doi.org/10.33927/hjic-2022-20.

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PC-FMEA is a method that combines the pairwise comparison and basic FMEA (Failure Modes and Effects Analysis) methods. Using the pairwise comparison, which of the risks is more severe, common or noticeable can be determined. The results evaluated by the pairwise comparison can be modeled with networks, where the risks can be ranked according to the criteria using the PageRank and weighted in-degree values. Applying these two solutions together, a form of risk assessment can be created where risks are assessed by pairwise comparisons and the results analyzed using network research tools. The re

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Yakovlev, P. A. "Fast trie-based method for multiple pairwise sequence alignment." Доклады Академии наук 484, no. 4 (2019): 401–4. http://dx.doi.org/10.31857/s0869-56524844401-404.

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A method for efficient comparison of a symbol sequence with all strings of a set is presented, which performs considerably faster than the naive enumeration of comparisons with all strings in succession. The procedure is accelerated by applying an original algorithm combining a prefix tree and a standard dynamic programming algorithm searching for the edit distance (Levenshtein distance) between strings. The efficiency of the method is confirmed by numerical experiments with arrays consisting of tens of millions of biological sequences of variable domains of monoclonal antibodies.

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Wang, Haichao, Risto Lahdelma, and Pekka Salminen. "Complementary Judgment Matrix Method with Imprecise Information for Multicriteria Decision-Making." Mathematical Problems in Engineering 2018 (October 9, 2018): 1–11. http://dx.doi.org/10.1155/2018/3695627.

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The complementary judgment matrix (CJM) method is an MCDA (multicriteria decision aiding) method based on pairwise comparisons. As in AHP, the decision-maker (DM) can specify his/her preferences using pairwise comparisons, both between different criteria and between different alternatives with respect to each criterion. The DM specifies his/her preferences by allocating two nonnegative comparison values so that their sum is 1. We measure and pinpoint possible inconsistency by inconsistency errors. We also compare the consistency of CJM and AHP trough simulation. Because preference judgments ar

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Jin, Fengxia, Zhonghua Wu, Kun Zhao, Juan L. G. Guirao, and Huatao Chen. "The Determination Method of Satisfactory Consistency of the Interval Number Pairwise Comparisons Matrix Based on Submatrix." Entropy 24, no. 12 (2022): 1795. http://dx.doi.org/10.3390/e24121795.

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The decision-maker obtains the pairwise comparisons matrix by comparing two entities. In the process of comparing the two entities, the relationship between the two entities and other entities is not considered. In this way, the judgment may be illogical. This paper mainly studies the satisfactory consistency of the interval number pairwise comparisons matrix based on cyclic matrix. Firstly, the illogical judgment entity in the process of the decision-maker’s judgment is expressed by the cyclic matrix. There are three entities and four entities to form the cyclic matrix. The relationship and v

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Kułakowski, Konrad. "Heuristic Rating Estimation Approach to The Pairwise Comparisons Method." Fundamenta Informaticae 133, no. 4 (2014): 367–86. http://dx.doi.org/10.3233/fi-2014-1081.

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Kułakowski, Konrad. "On the Geometric Mean Method for Incomplete Pairwise Comparisons." Mathematics 8, no. 11 (2020): 1873. http://dx.doi.org/10.3390/math8111873.

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One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for

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González-Pachón, Jacinto, and Carlos Romero. "A method for dealing with inconsistencies in pairwise comparisons." European Journal of Operational Research 158, no. 2 (2004): 351–61. http://dx.doi.org/10.1016/j.ejor.2003.06.009.

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Vargas, Luis G. "Utility Theory and reciprocal pairwise comparisons: The Eigenvector Method." Socio-Economic Planning Sciences 20, no. 6 (1986): 387–91. http://dx.doi.org/10.1016/0038-0121(86)90051-0.

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Bao, Jianzhu, Bojun Jin, Yang Sun, Yice Zhang, Yuhang He, and Ruifeng Xu. "A Comparison-Based Framework for Argument Quality Assessment." Electronics 13, no. 20 (2024): 4088. http://dx.doi.org/10.3390/electronics13204088.

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Assessing the quality of arguments is both valuable and challenging. Humans often find that making pairwise comparisons between a target argument and several reference arguments facilitates a more precise judgment of the target argument’s quality. Inspired by this, we propose a comparison-based framework for argument quality assessments (CompAQA), which scores the quality of an argument through multiple pairwise comparisons. Additionally, we introduce an argument order-based data augmentation strategy to enhance CompAQA’s relative quality comparison ability. By introducing multiple reference a

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Krivulin, Nikolai K., Temirlan Abildaev, Vladlena D. Gorshechnikova, Deivid Kapatsa, Elizaveta A. Magdich, and Anastasia A. Mandrikova. "On Solving Multicriteria Decision Making Problems Based on Pairwise Comparisons." Computer tools in education, no. 2 (June 27, 2020): 27–58. http://dx.doi.org/10.32603/2071-2340-2020-2-27-58.

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Problems known in the literature are considered for evaluating ratings of alternatives based on pairwise comparisons. To solve the problems, three methods are used, including the traditional method of of analysis of hierarchies by T. Saaty and the method of weighted geometric means, as well as the new method of minimax log-Chebyshev approximation, for which the solution is obtained using the apparatus and methods of tropical (idempotent) mathematics. Comparison of the solutions obtained shows that the use of different methods does not always lead to the same or close results. If the results of

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Huang, Han-Chen, and Xiaojun Yang. "Pairwise Comparison and Distance Measure of Hesitant Fuzzy Linguistic Term Sets." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/954040.

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A hesitant fuzzy linguistic term set (HFLTS), allowing experts using several possible linguistic terms to assess a qualitative linguistic variable, is very useful to express people’s hesitancy in practical decision-making problems. Up to now, a little research has been done on the comparison and distance measure of HFLTSs. In this paper, we present a comparison method for HFLTSs based on pairwise comparisons of each linguistic term in the two HFLTSs. Then, a distance measure method based on the pairwise comparison matrix of HFLTSs is proposed, and we prove that this distance is equal to the di

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Lakicevic, Milena, Keith Reynolds, and Bojan Srdjevic. "Assessing landscape plans with abbreviated pair-wise comparisons in the AHP (Analitic Hierarchy Process)." Zbornik Matice srpske za prirodne nauke, no. 136 (2019): 183–94. http://dx.doi.org/10.2298/zmspn1936183l.

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This paper demonstrates the application of the Analytic Hierarchy Pro?cess (AHP) in assessing landscape plans using the option of abbreviated pair-wise comparisons to simplify the weight elicitation process for decision makers. Whereas the standard AHP elicitation procedure requires a full set of pairwise comparisons among all criteria at each node of the decision hierarchy in order to derive criterion weights for the decision model, the abbreviated pairwise method uses a minimal spanning set of pairwise comparisons, and remaining comparisons are then derived by transitivity rules. In this pap

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Čančer, Vesna. "Selection Procedure of the Approximation Methods for Deriving Priorities: A Case of Inconsistent Pairwise Comparisons." Business Systems Research Journal 15, no. 2 (2024): 21–30. http://dx.doi.org/10.2478/bsrj-2024-0015.

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Abstract Background When pairwise comparisons are used to express preferences for alternatives or judgments on criteria's importance, several methods can be used to derive priorities in multi-criteria decision-making. In the case of inconsistency, different methods give different results. Objectives The main goal of this paper is to present the procedure of measuring the accuracy of the selected approximation methods based on pairwise comparisons compared to the priorities obtained by the eigenvalue method. It also aims to illustrate the procedure on the numerical example characterised by acce

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FEDRIZZI, MICHELE, and MATTEO BRUNELLI. "FAIR CONSISTENCY EVALUATION FOR RECIPROCAL RELATIONS AND IN GROUP DECISION MAKING." New Mathematics and Natural Computation 05, no. 02 (2009): 407–20. http://dx.doi.org/10.1142/s1793005709001398.

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In decision-making processes, it often occurs that the decision maker is asked to pairwise compare alternatives. His/her judgements over a set of pairs of alternatives can be collected into a matrix and some relevant properties, for instance, consistency, can be estimated. Consistency is a desirable property which implies that all the pairwise comparisons respect a principle of transitivity. So far, many indices have been proposed to estimate consistency. Nevertheless, in this paper we argue that most of these indices do not fairly evaluate this property. Then, we introduce a new consistency e

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Kułakowski, Konrad. "A heuristic rating estimation algorithm for the pairwise comparisons method." Central European Journal of Operations Research 23, no. 1 (2013): 187–203. http://dx.doi.org/10.1007/s10100-013-0311-x.

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Kułakowski, Konrad, Jacek Szybowski, Jiri Mazurek, and Sebastian Ernst. "Resilient heuristic aggregation of judgments in the pairwise comparisons method." Information Sciences 657 (February 2024): 119979. http://dx.doi.org/10.1016/j.ins.2023.119979.

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Mukhametzyanov, Irik Z. "Transformation of numerical scales for pairwise comparisons: AHP, Dematel, BWM, SWARA." Journal Of Applied Informatics 17, no. 5 (2022): 15–33. http://dx.doi.org/10.37791/2687-0649-2022-17-5-15-33.

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The paper presents an overview and comparative analysis of four weighting methods for multi-criteria decision-making problem based on pairwise comparisons: AHP, Dematel, BWM and SWARA. It is demonstrate, by examples that the reliability of evaluations largely depends on the correct use of the pairwise comparison tool: evaluations are given on a verbal scale, then converted into quantitative values and then the criteria priorities are calculated. All stages of pairwise comparisons are multivariate. In particular, the validity of this decision-making tool depends on the choice of numerical scale

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Dvoenko, Sergey D. "Metric correctness of pairwise comparisons in intelligent data analysis." Control and Cybernetics 52, no. 3 (2023): 291–334. http://dx.doi.org/10.2478/candc-2023-0040.

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Abstract In modern data analysis and machine learning, data are often represented in the form of pairwise comparisons of the elements of the data set. The pairwise comparisons immediately correspond to the similarity or dissimilarity of objects under investigation, and such a situation regularly arises in the domains of image and signal analysis, bioinformatics, expert evaluation, etc. The practical pairwise comparison functions may be incorrect in terms of potentially using them as scalar products or distances. In contrast to other approaches, we develop in this paper a technique based on the

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Song, Bangweon, and Seokjoong Kang. "A Method of Assigning Weights Using a Ranking and Nonhierarchy Comparison." Advances in Decision Sciences 2016 (April 28, 2016): 1–9. http://dx.doi.org/10.1155/2016/8963214.

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The analytic hierarchy process (AHP) has advantages that the whole number of comparisons can be reduced via a hierarchy structure and the consistency of responses verified via a consistency ratio. However, at the same time, the AHP has disadvantages that values vary according to the form of hierarchy structure and it is difficult to maintain consistency itself among responses. If the number of comparisons can be reduced, a comparison within a single level is optimal, and if comparison can be made while the priority among entities is maintained, consistency may be automatically maintained. Thus

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Vasconcelos, Giancarllo Ribeiro, and Caroline Maria de Miranda Mota. "Exploring Multicriteria Elicitation Model Based on Pairwise Comparisons: Building an Interactive Preference Adjustment Algorithm." Mathematical Problems in Engineering 2019 (June 18, 2019): 1–14. http://dx.doi.org/10.1155/2019/2125740.

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Pairwise comparisons have been applied to several real decision making problems. As a result, this method has been recognized as an effective decision making tool by practitioners, experts, and researchers. Although methods based on pairwise comparisons are widespread, decision making problems with many alternatives and criteria may be challenging. This paper presents the results of an experiment used to verify the influence of a high number of preferences comparisons in the inconsistency of the comparisons matrix and identifies the influence of consistencies and inconsistencies in the assessm

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Tkachenko, Maksim, and Hady W. Lauw. "CompareLDA: A Topic Model for Document Comparison." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7112–19. http://dx.doi.org/10.1609/aaai.v33i01.33017112.

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A number of real-world applications require comparison of entities based on their textual representations. In this work, we develop a topic model supervised by pairwise comparisons of documents. Such a model seeks to yield topics that help to differentiate entities along some dimension of interest, which may vary from one application to another. While previous supervised topic models consider document labels in an independent and pointwise manner, our proposed Comparative Latent Dirichlet Allocation (CompareLDA) learns predictive topic distributions that comply with the pairwise comparison obs

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Sapin, Emmanuel, and Matthew C. Keller. "Novel approach for parallelizing pairwise comparison problems as applied to detecting segments identical by decent in whole-genome data." Bioinformatics 37, no. 15 (2021): 2121–25. http://dx.doi.org/10.1093/bioinformatics/btab084.

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Abstract Motivation Pairwise comparison problems arise in many areas of science. In genomics, datasets are already large and getting larger, and so operations that require pairwise comparisons—either on pairs of SNPs or pairs of individuals—are extremely computationally challenging. We propose a generic algorithm for addressing pairwise comparison problems that breaks a large problem (of order n2 comparisons) into multiple smaller ones (each of order n comparisons), allowing for massive parallelization. Results We demonstrated that this approach is very efficient for calling identical by desce

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Dorton, Steve, Ian Frommer, Margaret Bailey, and Teresita Sotomayor. "Prioritizing Design Goals for a Medical Simulator Using Pairwise Comparisons." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 62, no. 1 (2018): 1648–52. http://dx.doi.org/10.1177/1541931218621374.

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A simulator is being developed to teach psychomotor skills for the lateral canthotomy and cantholysis procedure to medical providers, filling a current training gap at military medical training facilities. Subject Matter Experts (SMEs) agree on training system design goals; however, there is a lack of consensus on the relative order and magnitude of the priorities of each goal. The designs and implementations to achieve each goal have several interdependencies and tradeoffs, which require a comparison between different sets of design goals. A survey of pairwise comparisons was distributed to S

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Bondarenko, V., and M. Karanfilov. "DECISION-MAKING PROBLEMS IN PUBLIC TENDERS TO ASSESS THE COMPANIES-BIDDERS." Grail of Science, no. 17 (August 4, 2022): 232–40. http://dx.doi.org/10.36074/grail-of-science.22.07.2022.041.

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The article is devoted to the development of a decision support system in a Purchase Tender. Such the system allows an institution that announced a Purchase Tender to estimate suppliers that have an interest in supply and can take part in such tender offering different conditions of purchase. The main method that is used to build a decision support system was chosen as the method of the analytic hierarchy process that was developed by T.L. Saaty based on construction pairwise comparisons matrices of suppliers and their features. Such matrices are constructed by experts and they need for cohere

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Noghin, V. D. "Fuzzy Extension of Simplified variant of AHP." Journal of Physics: Conference Series 2060, no. 1 (2021): 012019. http://dx.doi.org/10.1088/1742-6596/2060/1/012019.

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Abstract A class of methods for ranking a finite set of objects based on a multiplicative matrix of pairwise comparisons, when the comparison results are expressed by fuzzy values, is considered. A fuzzy extension of the simplified version of the AHP, which was introduced by the author earlier, is proposed. In this extension, the elements of the matrix of pairwise comparisons can be type 1 or type 2 fuzzy numbers.

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Koczkodaj, Waldemar W. "Statistically Accurate Evidence of Improved Error Rate by Pairwise Comparisons." Perceptual and Motor Skills 82, no. 1 (1996): 43–48. http://dx.doi.org/10.2466/pms.1996.82.1.43.

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A statistical experiment was designed to check whether the pairwise comparisons method, introduced by Thurstone in 1927, can really improve the accuracy of estimation of stimuli. This method was compared with direct rating. The experiment was designed and implemented to minimize statistical bias. Randomly generated bars were used since everyone is an expert on estimating lengths. The statistical analysis favoured the pairwise comparisons method The obtained results are decisive; more than a 300% improvement in accuracy was gained with at least 10 level of confidence.

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German, O. V., Ju O. German, and М. V. Kuznetsov. "Evaluation of Control Priorities Based on a Matrix of Paired Comparisons." Doklady BGUIR 20, no. 2 (2022): 62–70. http://dx.doi.org/10.35596/1729-7648-2022-20-2-62-70.

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The article contains a description of the model and approach for determining the weights of controls (other objects) based on a matrix of pairwise comparisons. The initial data in the matrix of paired comparisons implicitly specify interval estimates for comparison of controls. Interval estimates can be constructed relatively easily using Harrington's fuzzy metric scale. A heuristic method for determining the priorities of controls is proposed, which seeks to obtain weights (priorities) of controls that deviate minimally from the boundary values of the weight intervals.The latter are easy to f

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Rodríguez Montequín, Vicente, Joaquín Manuel Villanueva Villanueva Balsera, Marina Díaz Piloñeta, and César Álvarez Pérez. "A Bradley-Terry Model-Based Approach to Prioritize the Balance Scorecard Driving Factors: The Case Study of a Financial Software Factory." Mathematics 8, no. 2 (2020): 276. http://dx.doi.org/10.3390/math8020276.

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The prioritization of factors has been widely studied applying different methods from the domain of the multiple-criteria decision-making, such as for example the Analytic Hierarchy Process method (AHP) based on decision-makers’ pairwise comparisons. Most of these methods are subjected to a complex analysis. The Bradley-Terry model is a probability model for paired evaluations. Although this model is usually known for its application to calculating probabilities, it can be also extended for ranking factors based on pairwise comparison. This application is much less used; however, this work sho

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GHOLAMIAN, M. R., S. M. T. FATEMI GHOMI, and M. GHAZANFARI. "FARSJUM, A FUZZY SYSTEM FOR RANKING SPARSE JUDGMENT MATRICES: A CASE STUDY IN SOCCER TOURNAMENTS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 01 (2007): 115–29. http://dx.doi.org/10.1142/s0218488507004406.

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The establishment of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). However, the number of pairwise comparisons necessary in real problems often becomes overwhelming. In such cases, generally the experts are not able to answer all questions and consequently sparse judgment matrix is generated which caused "equal ranks" and "rank reversal" based on AHP method. In this paper, a new ranking system (FARSJUM) is developed for such sparse judgment matrix. The system is constructed on fuzzy rules and fuzzy reasoning methods. The nume

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Surkov, A. A. "Application of the Method of Pairwise Comparisons When Combining Economic Forecasts." Accounting. Analysis. Auditing 6, no. 3 (2019): 32–42. http://dx.doi.org/10.26794/2408-9303-2019-6-3-32-42.

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The method of combining forecasts has already proven itself in practice as a reliable and effective way to improve the accuracy of economic forecasting. But this technique has several disadvantages. Today, one of the ways to improve the method of combining forecasts is to find the possibility of attracting expert information as a tool for correcting the obtained forecast results. This article is devoted to the use of an expert method of pairwise comparisons for constructing the weights of the combined forecast as one of the options for which you can use expert information when combining foreca

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Geman, Donald, Christian d'Avignon, Daniel Q. Naiman, and Raimond L. Winslow. "Classifying Gene Expression Profiles from Pairwise mRNA Comparisons." Statistical Applications in Genetics and Molecular Biology 3, no. 1 (2004): 1–19. http://dx.doi.org/10.2202/1544-6115.1071.

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We present a new approach to molecular classification based on mRNA comparisons. Our method, referred to as the top-scoring pair(s) (TSP) classifier, is motivated by current technical and practical limitations in using gene expression microarray data for class prediction, for example to detect disease, identify tumors or predict treatment response. Accurate statistical inference from such data is difficult due to the small number of observations, typically tens, relative to the large number of genes, typically thousands. Moreover, conventional methods from machine learning lead to decisions wh

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Pan, Dongbo, Xi Lu, Juan Liu, and Yong Deng. "A Ranking Procedure by Incomplete Pairwise Comparisons Using Information Entropy and Dempster-Shafer Evidence Theory." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/904596.

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Decision-making, as a way to discover the preference of ranking, has been used in various fields. However, owing to the uncertainty in group decision-making, how to rank alternatives by incomplete pairwise comparisons has become an open issue. In this paper, an improved method is proposed for ranking of alternatives by incomplete pairwise comparisons using Dempster-Shafer evidence theory and information entropy. Firstly, taking the probability assignment of the chosen preference into consideration, the comparison of alternatives to each group is addressed. Experiments verified that the informa

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ICHIHASHI, Hidetomo. "A Quantification Method of Pairwise Comparisons by Neuro-Like Fuzzy Modeling." Journal of Japan Society for Fuzzy Theory and Systems 4, no. 5 (1992): 958–67. http://dx.doi.org/10.3156/jfuzzy.4.5_958.

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Lee, Dong-Hee, Kwang-Jae Kim, and Murat Köksalan. "An interactive method to multiresponse surface optimization based on pairwise comparisons." IIE Transactions 44, no. 1 (2012): 13–26. http://dx.doi.org/10.1080/0740817x.2011.564604.

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Kułakowski, Konrad. "Inconsistency in the ordinal pairwise comparisons method with and without ties." European Journal of Operational Research 270, no. 1 (2018): 314–27. http://dx.doi.org/10.1016/j.ejor.2018.03.024.

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Тен, R. Ten, Карпин, et al. "Matrix of pairwise comparisons of samples in evaluation of the effect of dosed physical load on the body by." Journal of New Medical Technologies. eJournal 10, no. 1 (2016): 0. http://dx.doi.org/10.12737/18450.

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The parameters of cardiovascular and neuromuscular systems in untrained and trained subjects by the methods of classical statistics in terms of the influence of physical activity are examined. A new method of matrices of pairwise comparisons of samples, which allows to evaluate the effect of exercise on the human body is proposed. Calculation of matrices of pairwise comparisons of samples of trained subjects before and after exer-cise showed a decrease in the number of random pairs of samples of RR-intervals that are (pairs of) can be attri-buted to a single population, indicating a stabilizin

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Karkour, Youssef, Chakir Tajani, and Idriss Khattabi. "Generating a Set of Consistent Pairwise Comparison Test Matrices in AHP using Particle Swarm Optimization." WSEAS TRANSACTIONS ON MATHEMATICS 23 (April 1, 2024): 206–15. http://dx.doi.org/10.37394/23206.2024.23.24.

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Pairwise Comparison Matrix (PCM) play a crucial role in multi-criteria decision-making, especially within the framework of the Analytic Hierarchy Process (AHP). It is essential for an expert to systematically assess and compare alternatives, considering various criteria as part of the decision-making process. The AHP relies on consistency to ensure the accuracy of pairwise comparisons made by decision makers, increasing the overall integrity of the decision-making process. The aim of this paper is to present an approach based on Particle Swarm Optimization (PSO) as a metaheuristic method to ge

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Moslem, Sarbast, Ahmad Alkharabsheh, Karzan Ismael, and Szabolcs Duleba. "An Integrated Decision Support Model for Evaluating Public Transport Quality." Applied Sciences 10, no. 12 (2020): 4158. http://dx.doi.org/10.3390/app10124158.

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Big cities suffer from serious complex problems such as air pollution, congestion, and traffic accidents. Developing public transport quality in such cities is considered an efficient remedy to obviate these critical issues. This paper aims to determine the significant supply quality criteria of public transportation. As a methodology, a hybrid Analytic Hierarchy Process (AHP) combined with the Best Worst Method (BWM) is applied. The proposed model is basically a hierarchy structure with at least a 5 × 5 pairwise comparison matrix or larger. A real-world complex problem was examined to validat

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Ahmad, Qazi Shoeb, Mohammad Faisal Khan, and Naeem Ahmad. "Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment." Axioms 11, no. 11 (2022): 659. http://dx.doi.org/10.3390/axioms11110659.

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The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it uses fewer calculations and analyses while maintaining good, acceptable consistency ratio values. A multi-choice best–worst method (MCBWM), which considers several options for pairwise comparison of preferences between the criteria, has recently been developed. The experts are given the optio

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Feng, Xiang-Qian, Xiao-Dong Pang, and Cui-Ping Wei. "Distance-Based Consistency Measure and Priority Weights of Best-Worst Multi-Criteria Decision Making Method." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 05 (2020): 853–78. http://dx.doi.org/10.1142/s0218488520500373.

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Best-Worst method (BWM) is a new multi-criteria decision-making method based on pairwise comparisons, but only the comparisons concerning the best and the worst alternatives or criteria. This method shows some significant advantages in the simplicity with a less requirement of comparison data and reliability with better consistency. This paper proposes a new consistency measure method based on the distance of the vectors of reference comparisons in BWM because the difference of the preference in two vectors directly affects the reliability of results. Through the establishment of the threshold

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Pamučar, Dragan, Željko Stević, and Siniša Sremac. "A New Model for Determining Weight Coefficients of Criteria in MCDM Models: Full Consistency Method (FUCOM)." Symmetry 10, no. 9 (2018): 393. http://dx.doi.org/10.3390/sym10090393.

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In this paper, a new multi-criteria problem solving method—the Full Consistency Method (FUCOM)—is proposed. The model implies the definition of two groups of constraints that need to satisfy the optimal values of weight coefficients. The first group of constraints is the condition that the relations of the weight coefficients of criteria should be equal to the comparative priorities of the criteria. The second group of constraints is defined on the basis of the conditions of mathematical transitivity. After defining the constraints and solving the model, in addition to optimal weight values, a

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Nefedov, A. S., V. A. Shakirov, and S. M. Ignatieva. "Multi-criteria selection of the mix of generating plants in local energy systems based on a modified analytic hierarchy process." iPolytech Journal 26, no. 3 (2022): 451–64. http://dx.doi.org/10.21285/1814-3520-2022-3-451-464.

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This paper presents a modification of the analytic hierarchy process in order to increase its efficiency for a multi-criteria comparison of mixes of generating plants in local energy areas during their development. The multi-criteria problem of selecting the most effective ratio of rated capacities is considered for power plants representing a single mix of generating plants during the development of a local energy area in the Khabarovsk Krai. The energy sources are represented by thermal, solar, wind and diesel power plants. The following estimation criteria for alternative solutions were acc

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