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## Archive of Issues

Russia Chelyabinsk
Year
2019
Volume
29
Issue
2
Pages
197-210
 Section Mathematics Title Comparison of triangular fuzzy numbers Author(-s) Ukhobotov V.I.a, Stabulit I.S.ab, Kudryavtsev K.N.ab Affiliations Chelyabinsk State Universitya, South Ural State Universityb Abstract Difficulties in comparing fuzzy numbers occur in many applied problems. There are different approaches to dealing with the above difficulties. These approaches are determined by the specificity of the problems under consideration. The approach proposed in this article for comparing fuzzy numbers is as follows. First, a rule is constructed for comparing a real number with the $\alpha$-level set of a fuzzy number. Then, using the procedure of averaging over $\alpha$, a rule is constructed for comparing a real number with a fuzzy number. By means of the procedure for separating two fuzzy numbers with the help of a real number, a rule for comparing fuzzy numbers is introduced. Based on the developed approach, the rule for defuzzification of fuzzy numbers is proposed. As an example, triangular fuzzy numbers are considered. Keywords comparison of fuzzy numbers, defuzzification, triangular fuzzy numbers UDC 519.816 MSC 03B52, 68T37 DOI 10.20537/vm190205 Received 21 March 2019 Language Russian Citation Ukhobotov V.I., Stabulit I.S., Kudryavtsev K.N. Comparison of triangular fuzzy numbers, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 2, pp. 197-210. References Zadeh L.A. Fuzzy sets, Information and Control, 1965, vol. 8, no. 3, pp. 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X Zadeh L.A. Fuzzy logic, Computer, 1988, vol. 21, no. 4, pp. 83-93. https://doi.org/10.1109/2.53 Zimmermann H.-J. Fuzzy set theory - and its applications, Dordrecht: Springer, 2001. https://doi.org/10.1007/978-94-010-0646-0 Kosko B. Fuzzy systems as universal approximators, IEEE Transactions on Computers, 1994, vol. 43, no. 11, pp. 1329-1333. https://doi.org/10.1109/12.324566 Li L., Lai K.K. A fuzzy approach to the multiobjective transportation problem, Computers and Operations Research, 2000, vol. 27, no. 1, pp. 43-57. https://doi.org/10.1016/S0305-0548(99)00007-6 Chen C.-T., Lin C.-T., Huang S.-F. A fuzzy approach for supplier evaluation and selection in supply chain management, International Journal of Production Economics, 2006, vol. 102, no. 2, pp. 289-301. https://doi.org/10.1016/j.ijpe.2005.03.009 Bahri O., Talbi E.-G., Amor N.B. A generic fuzzy approach for multi-objective optimization under uncertainty, Swarm and Evolutionary Computation, 2018, vol. 40, pp. 166-183. https://doi.org/10.1016/j.swevo.2018.02.002 Korzhov A.V., Korzhova M.E. A method of accounting for fuzzy operational factors influencing 6 (10) kV power cable insulation longevity, 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), IEEE, Chelyabinsk, 2016, pp. 1-4. https://doi.org/10.1109/ICIEAM.2016.7911429 Larbani M. Non cooperative fuzzy games in normal form: A survey, Fuzzy Sets and Systems, 2009, vol. 160, no. 22, pp. 3184-3210. https://doi.org/10.1016/j.fss.2009.02.026 Kudryavtsev K.N., Stabulit I.S., Ukhobotov V.I. A bimatrix game with fuzzy payoffs and crisp game, CEUR Workshop Proceedings, 2017, vol. 1987, pp. 343-349. Kudryavtsev K.N., Stabulit I.S., Ukhobotov V.I. One approach to fuzzy matrix games, CEUR Workshop Proceedings, 2018, vol. 2098, pp. 228-238. Verma T., Kumar A. Ambika methods for solving matrix games with Atanassov's intuitionistic fuzzy payoffs, IEEE Transactions on Fuzzy Systems, 2018, vol. 26, no. 1, pp. 270-283. https://doi.org/10.1109/TFUZZ.2017.2651103 Dutta P., Boruah H., Ali T. Fuzzy arithmetic with and without using $\alpha$-cut method: A comparative study, International Journal of Latest Trends in Computing, 2011, vol. 2, no. 1, pp. 99-107. Bansal A. Trapezoidal fuzzy numbers $(a, b, c, d)$: arithmetic behavior, International Journal of Physical and Mathematical Sciences, 2011, vol. 2, no. 1, pp. 39-44. Gallyamov E.R., Ukhobotov V.I. Computer implementation of operations with fuzzy numbers, Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya “Vychislitelnaya Matematika i Informatika”, 2014, vol. 3, no. 3, pp. 97-108 (in Russian). https://doi.org/10.14529/cmse140306 Yager R.R. A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 1981, vol. 24, no. 2, pp. 143-161. https://doi.org/10.1016/0020-0255(81)90017-7 Ibáñez L.M.C., Muñoz A.G. A subjective approach for ranking fuzzy numbers, Fuzzy Sets and Systems, 1989, vol. 29, no. 2, pp. 145-153. https://doi.org/10.1016/0165-0114(89)90188-7 Chen S.-J., Hwang C.-L. Fuzzy multiple attribute decision making methods, Fuzzy multiple attribute decision making, Berlin-Heidelberg: Springer, 1992, pp. 289-486. https://doi.org/10.1007/978-3-642-46768-4_5 Ukhobotov V.I., Shchichko P.V. An approach to ranking fuzzy numbers, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2011, issue 10, pp. 54-62 (in Russian). http://mi.mathnet.ru/eng/vyuru185 Ukhobotov V.I., Mikhailova E.S. An approach to the comparison of fuzzy numbers in decision-making problems, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2015, vol. 7, no. 1, pp. 32-37 (in Russian). http://mi.mathnet.ru/eng/vyurm208 Ukhobotov V.I., Mikhailova E.S. Comparison of fuzzy numbers in decision-making problems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 87-94 (in Russian). https://doi.org/10.20537/vm160108 Ukhobotov V.I. Izbrannye glavy teorii nechetkikh mnozhestv: uchebnoe posobie (The selected chapters of the theory of fuzzy sets: study guide), Chelyabinsk: Chelyabinsk State University, 2011. Full text