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Reasonable properties for the ordering of fuzzy quantities. I. (English) Zbl 0971.03054
In the literature more than 35 tentatives of solving the problem of ordering fuzzy quantities are presented. They can be classified into three categories: using the defuzzification indices; comparision with reference quantities; based on a fuzzy relation. In this paper the first and the second category are briefly presented. A set of axioms for an ordering approach is proposed and the presented variants are analysed from the point of view of these axioms.
Reviewer: Ioan Tofan (Iaşi)

03E72 Theory of fuzzy sets, etc.
06A99 Ordered sets
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[1] Adamo, J.M., Fuzzy decision trees, Fuzzy sets and systems, 4, 207-219, (1980) · Zbl 0444.90004
[2] Baas, S.M.; Kwakernaak, H., Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13, 47-58, (1977) · Zbl 0363.90010
[3] Baldwin, J.F.; Guild, N.C.F., Comparison of fuzzy sets on the same decision space, Fuzzy sets and systems, 2, 213-231, (1979) · Zbl 0422.90004
[4] Bortolan, G.; Degni, R., A review of some methods for ranking fuzzy subsets, Fuzzy sets and systems, 15, 1-19, (1985) · Zbl 0567.90056
[5] Campos, L.; Munoz, A., A subjective approach for ranking fuzzy numbers, Fuzzy sets and systems, 29, 145-153, (1989) · Zbl 0672.90001
[6] W. Chang, Ranking of fuzzy utilities with triangular membership functions, Proceedings of International Conference on Policy Analysis and Systems, 1981, pp. 263-272.
[7] Chen, S., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy sets and systems, 17, 113-129, (1985) · Zbl 0618.90047
[8] Choobineh, F.; Li, H., An index for ordering fuzzy numbers, Fuzzy sets and systems, 54, 287-294, (1993)
[9] Efstathiou, J.; Tong, R.M., Ranking fuzzy sets: a decision theoretic approach, IEEE trans. systems man cybernet., 12, 655-659, (1982)
[10] Fortemps, P.; Roubens, M., Ranking and defuzzification methods based on area compensation, Fuzzy sets and systems, 82, 319-330, (1996) · Zbl 0886.94025
[11] Freeling, S., Fuzzy sets and decision analysis, IEEE trans. systems man cybernet., 10, 341-354, (1980)
[12] Jain, R., A procedure for multiple-aspect decision making using fuzzy set, Internat. J. systems sci., 8, 1-7, (1977) · Zbl 0347.90001
[13] Jain, R., Decision making in the presence of fuzzy variables, IEEE trans. systems man cybernet., SMC-6, 698-703, (1976) · Zbl 0337.90005
[14] Kerre, E., The use of fuzzy set theory in eletrocardiological diagnostics, (), 277-282
[15] Kim, K.; Park, K.S., Ranking fuzzy numbers with index of optimism, Fuzzy sets and systems, 35, 143-150, (1990)
[16] Liou, T.; Wang, J., Ranking fuzzy numbers with integral value, Fuzzy sets and systems, 50, 247-255, (1992) · Zbl 1229.03043
[17] Saade, J.J.; Schwarzlander, H., Ordering fuzzy sets over the real line: an approach based on decision making under uncertainty, Fuzzy sets and systems, 50, 237-246, (1992)
[18] Tong, R.M.; Bonissone, P.P., A linguistic approach between fuzzy numbers and its use in fuzzy sets, IEEE trans. systems man cybernet., 10, 716-723, (1980)
[19] X. Wang, A comparative study of the ranking methods for fuzzy quantities, Ph.D. Thesis, University of Ghent, 1997.
[20] Wang, X.; Kerre, E., On the classification and the dependencies of the ordering methods, (), 73-88
[21] X. Wang, A class of approaches to ordering alternatives, MSc Thesis, Taiyuan University of Technology, 1987 (in Chinese).
[22] R.R. Yager, Ranking fuzzy subsets over the unit interval, Proc. CDC (1978) 1435-1437.
[23] Yager, R.R., On choosing between fuzzy subsets, Kybernetes, 9, 151-154, (1980) · Zbl 0428.03050
[24] Yager, R.R., A procedure for ordering fuzzy sets of the unit interval, Inform. sci., 24, 143-161, (1981) · Zbl 0459.04004
[25] Yuan, Y., Criteria for evaluating fuzzy ranking methods, Fuzzy sets and systems, 43, 139-157, (1991) · Zbl 0747.90003
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