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Ranking fuzzy numbers with integral value. (English) Zbl 1229.03043
Summary: Ranking fuzzy numbers is important in decision making. Since very often the alternatives are evaluated by fuzzy numbers in a vague environment, a comparison between these fuzzy numbers is indeed a comparison between alternatives. We propose here a method of ranking fuzzy numbers with integral value. The method, which is independent of the type of membership functions used and the normality of the functions, can rank more than two fuzzy numbers simultaneously. It is relatively simple in computation, especially in ranking triangular and trapezoidal fuzzy numbers. Further, an index of optimism is used to reflect the decision maker’s optimistic attitude. Discussion on comparative advantages is included.

##### MSC:
 03E72 Theory of fuzzy sets, etc. 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 91B06 Decision theory
##### Keywords:
index of optimism
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##### References:
 [1] Baas, S.M.; Kwakernaak, H., Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13, 47-58, (1977) · Zbl 0363.90010 [2] Baldwin, J.F.; Guild, N.C.F., Comments on the fuzzy MAX operator of dubios and prade, Internat. J. systems sci., 10, 1063-1064, (1979) · Zbl 0406.94023 [3] Bortolan, G.; Degani, R., A review of some methods for ranking fuzzy numbers, Fuzzy sets and systems, 15, 1-19, (1985) · Zbl 0567.90056 [4] Chang, W., Ranking of fuzzy utilities with triangular membership functions, (), 263-272 [5] Chen, S.H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy sets and systems, 17, 113-129, (1985) · Zbl 0618.90047 [6] Dubois, D.; Prade, H., Operations on fuzzy numbers, Internat. J. systems sci., 9, 613-626, (1978) · Zbl 0383.94045 [7] Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic theory and applications, (1985), Van Nostrand Reinhold New York · Zbl 0588.94023 [8] Kim, K.; Park, K.S., Ranking fuzzy numbers with index of optimism, Fuzzy sets and systems, 35, 143-150, (1990) [9] Jain, R., A procedure for multi-aspect decision making using fuzzy sets, Internat. J. systems sci., 8, 1-7, (1978) · Zbl 0347.90001 [10] Schmucker, K.J., Fuzzy sets, natural language computations, and risk analysis, (1985), Computer Science Press Rockville, MD [11] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
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