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Russia Chelyabinsk
Year
2019
Volume
29
Issue
2
Pages
197-210
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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
  1. 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
  2. Zadeh L.A. Fuzzy logic, Computer, 1988, vol. 21, no. 4, pp. 83-93. https://doi.org/10.1109/2.53
  3. Zimmermann H.-J. Fuzzy set theory - and its applications, Dordrecht: Springer, 2001. https://doi.org/10.1007/978-94-010-0646-0
  4. 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
  5. 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
  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
  7. 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
  8. 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
  9. 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
  10. 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.
  11. Kudryavtsev K.N., Stabulit I.S., Ukhobotov V.I. One approach to fuzzy matrix games, CEUR Workshop Proceedings, 2018, vol. 2098, pp. 228-238.
  12. 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
  13. 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.
  14. 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.
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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.
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