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2019 | OriginalPaper | Chapter

On the Issue of Comparison of Fuzzy Numbers

Authors : Viktor Ukhobotov, Irina Stabulit, Konstantin Kudryavtsev

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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Abstract

In the class of decision-making problems with fuzzy information concerning criterion values, the problem of comparing fuzzy numbers is relevant. There are various approaches to solving it. They are determined by the specific character of the problem under consideration. This paper proposes one approach to comparing fuzzy numbers. The proposed approach is as follows. At first, a rule is constructed for comparing a real number with a level set of a fuzzy number. Then, with the help of a procedure for constructing the exact lower approximation for the collection of sets, a fuzzy set is constructed. This fuzzy set determine the rule for comparing a real number with a fuzzy number. Using this rule and the approach based on separating two fuzzy numbers with a real number, the procedure is chosen for comparing two fuzzy numbers. As an example, fuzzy numbers with trapezoidal membership functions are considered, and the geometric interpretation of the results being given.

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previous chapter The Accuracy of Approximate Solutions for a Boundary Value Inverse Problem with Final Overdetermination

Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1963)CrossRef

Zadeh, L.A.: Fuzzy logic. Computer 21(4), 83–93 (1988)CrossRef

Zimmermann, H.J.: Fuzzy Set Theory - and its Applications. Kluwer Academic Publishers, New York (1996)CrossRef

Kosko, B.: Fuzzy systems as universal approximators. IEEE Trans. Comput. 43(11), 1329–1333 (1994)CrossRef

Li, L., Lai, K.K.: A fuzzy approach to the multiobjective transportation problem. Comput. Oper. Res. 27(1), 43–57 (2000)MathSciNetCrossRef

Chen, C.T., Lin, C.T., Huang, S.F.: A fuzzy approach for supplier evaluation and selection in supply chain management. Int. J. Prod. Econ. 102(2), 289–301 (2006)CrossRef

Bahri, O., Talbi, E.G., Amor, N.B.: A generic fuzzy approach for multi-objective optimization under uncertainty. Swarm Evol. Comput. 40, 166–183 (2018)CrossRef

Korzhov, A.V., Korzhova, M.E.: A method of accounting for fuzzy operational factors influencing 6 (10) kV power cable insulation longevity. In: 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), pp. 1–4. IEEE, Chelyabinsk (2016). https://doi.org/10.1109/ICIEAM.2016.7911429

Larbani, M.: Non cooperative fuzzy games in normal form: a survey. Fuzzy Sets Syst. 160(22), 3184–3210 (2009)MathSciNetCrossRef

10.

Kudryavtsev, K.N., Stabulit, I.S., Ukhobotov, V.I.: A bimatrix game with fuzzy payoffs and crisp game. In: CEUR Workshop Proceedings 1987, pp. 343–349 (2017)

11.

Kudryavtsev, K.N., Stabulit, I.S., Ukhobotov, V.I.: One approach to fuzzy matrix games. In: CEUR Workshop Proceedings 2098, pp. 228–238 (2018)

12.

Verma, T., Kumar, A.: Ambika methods for solving matrix games with Atanassov’s intuitionistic fuzzy payoffs. IEEE Trans. Fuzzy Syst. 26(1), 270–283 (2018)CrossRef

13.

Dutta, P., Boruah, H., Ali, T.: Fuzzy arithmetic with and without using \(\alpha \)-cut method: a comparative study. Int. J. Latest Trends Comput. 2(1), 99–107 (2011)

14.

Bansal, A.: Trapezoidal fuzzy numbers (a, b, c, d): arithmetic behavior. Int. J. Phys. Math. Sci. 2(1), 39–44 (2011)MathSciNet

15.

Gallyamov, E.R., Ukhobotov, V.I.: Computer implementation of operations with fuzzy numbers. Bull. South Ural State Universit. 3(3), 97–108 (2014). Series “Vychislitelnaya Matematika i Informatika”. (in Russian)

16.

Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24(2), 143–161 (1981)MathSciNetCrossRef

17.

Ibanez, L.M.C., Munoz, A.G.: A subjective approach for ranking fuzzy numbers. Fuzzy Sets Syst. 29(2), 145–153 (1989)MathSciNetCrossRef

18.

Chen, S.J., Hwang, C.L.: Fuzzy multiple attribute decision making methods. In: Fuzzy Multiple Attribute Decision Making, pp. 289–486. Springer, Heidelberg (1992). https://doi.org/10.1007/978-3-642-46768-4_5CrossRef

19.

Ukhobotov, V.I., Shchichko, P.V.: An approach to ranking fuzzy numbers. Bull. South Ural State Universit. 10, 54–62 (2011). Series “Matematicheskoe modelirovanie I programmirovanie”. (in Russian)

20.

Ukhobotov, V.I., Mikhailova, E.S.: An approach to the comparison of fuzzy numbers in decision-making problems. Bull. South Ural State University 71, 32–37 (2015). Series “Mathematics. Mechanics. Physics”. (in Russian)MATH

21.

Ukhobotov, V.I., Mikhailova, E.S.: Comparison of fuzzy numbers in decision-making problems. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki 26(1), 87–94 (2016). https://doi.org/10.20537/vm160108. (in Russian)MathSciNetCrossRef

22.

Ukhobotov, V.I., Stabulit, I.S., Kudryavtsev, K.N.: Comparison of triangular fuzzy numbers. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki 29(2), 197–210 (2019). https://doi.org/10.20537/vm190205. (in Russian)CrossRef

23.

Ukhobotov, V.I., Stabulit, I.S., Kudryavtsev, K.N.: On decision making under fuzzy information about an uncontrolled factor. Procedia Comput. Sci. 150, 524–531 (2019). https://doi.org/10.1016/j.procs.2019.02.088CrossRef

24.

Ramik, J., Vlach, M.: Generalized Concavity in Fuzzy Optimization and Decision Analysis. Kluwer Academic Publishers, Boston (2001)MATH

25.

Ukhobotov, V.I.: The Selected Chapters of Fuzzy Set Theory: Study Guide. Chelyabinsk State University, Chelyabinsk (2011). (in Russian)

Title: On the Issue of Comparison of Fuzzy Numbers
Authors: Viktor Ukhobotov
Irina Stabulit
Konstantin Kudryavtsev
Publisher: Springer International Publishing
Book: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-33393-5

Electronic ISBN: 978-3-030-33394-2

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-33394-2_45

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