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DOI: https://doi.org/10.20537/vm160108

Abstract: The paper deals with decision-making problems, when a decision maker receives information about possible pay-off as a result of a strategy selection. This information can be given as a fuzzy number and the problem of its comparison appears. A specific character of the problem is a main factor to choose the method of the fuzzy numbers comparison. In this paper an approach of comparing fuzzy numbers has been proposed, it's based on the comparison of $\alpha$-cuts. These $\alpha$-cuts are segments. During the comparison of the segments, each segment can contain a merit value; one of the decision-making criteria is chosen (Wald's maximin model, Regret theory models, Routh–Hurwitz stability criterion etc.). The results of the comparison are averaged out. Fuzzy numbers are compared according to these mean values. According to geometrical interpretation which has been given, the comparison of fuzzy numbers is equivalent to the comparison of figures' areas. These areas are formed by graphics of membership functions of the fuzzy numbers. As an example trapezoidal and bell-shaped fuzzy numbers are examined.

Keywords: fuzzy number, membership function, level set.

Received: 25.02.2016

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Citation: V. I. Ukhobotov, E. S. Mikhailova, “Comparison of fuzzy numbers in decision-making problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016), 87–94

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https://www.mathnet.ru/eng/vuu521

https://www.mathnet.ru/eng/vuu/v26/i1/p87

This publication is cited in the following articles:

1. V. I. Ukhobotov, I. S. Stabulit, K. N. Kudryavtsev, “Sravnenie nechetkikh chisel treugolnogo vida”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 197–210      
2. Viktor Ukhobotov, Irina Stabulit, Konstantin Kudryavtsev, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 590  
3. V.I. Ukhobotov, I.S. Stabulit, K.N. Kudryavtsev, “On Decision Making under Fuzzy Information about an Uncontrolled Factor”, Procedia Computer Science, 150 (2019), 524  
4. Artyom Plyaskin, Alexey Kushniruk, Advances in Intelligent Systems and Computing, 1115, VIII International Scientific Siberian Transport Forum, 2020, 427  

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles