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Numerical representation of product transitive complete fuzzy orderings. (English) Zbl 1217.91037

Summary: Let \(X\) be a space of alternatives with a preference relation in the form of product transitive complete fuzzy ordering \(R\). We prove existence of continuous utility functions for \(R\).

MSC:

91B06 Decision theory
03E72 Theory of fuzzy sets, etc.
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References:

[1] Zadeh, L. A., Similarity relations and fuzzy orderings, Inform. Sci., 3, 2, 177-200 (1971) · Zbl 0218.02058
[2] Ponsard, C., Fuzzy mathematical models in economics, Fuzzy Sets and Systems, 28, 273-283 (1987) · Zbl 0657.90017
[3] Billot, A., An existence theorem for fuzzy utility functions: a new elementary proof, Fuzzy Sets and Systems, 74, 271-276 (1995) · Zbl 0858.90014
[4] Debreu, G., Theory of Value; An Axiomatic Analysis of Economic Equilibrium (1959), Wiley: Wiley New York · Zbl 0193.20205
[5] Fono, L. A.; Andjiga, N. G., Utility function of fuzzy preferences on a countable set under max-*-transitivity, J. Soc. Choice Welf., 28, 4, 667-683 (2007) · Zbl 1180.91122
[6] Cantor, G., Beiträge zur Begründung der transfiniten Megenlehre, Math. Ann., 46, 481-512 (1895) · JFM 26.0081.01
[7] Debreu, G., Representation of preference ordering by a numerical function, (Thrall, R. M.; Coombs, C. H.; Davis, R. L., Decision Processes (1954), Wiley: Wiley New York), 159-165
[8] Zadeh, L. A., Fuzzy sets, Inf. Control, 8, 338-353 (1965) · Zbl 0139.24606
[9] Nguyen, H. T.; Walker, E. A., Fuzzy Logic (2006), CRC Press
[10] Sengupta, K., Fuzzy preference and Orlovsky choice procedure, Fuzzy Sets and Systems, 93, 231-234 (1998) · Zbl 0930.91009
[11] Ovchinnikov, S. V., Numerical representations of transitive fuzzy relations, Fuzzy Sets and Systems, 126, 2, 225-232 (2002) · Zbl 0996.03510
[12] Campion, M. J.; Candeal, J. C.; Induráin, E., Representability of binary relations through fuzzy numbers, Fuzzy Sets and Systems, 157, 1-19 (2006) · Zbl 1117.03058
[13] Ćirić, M.; Ignjatović, J.; Bogdanovic, S., Fuzzy equivalence relations and their equivalence classes, Fuzzy Sets and Systems, 158, 12, 1295-1313 (2007) · Zbl 1123.03049
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