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A necessary and sufficient condition for the existence of Orlovsky’s choice set. (English) Zbl 0641.90007
Summary: In a previous paper [Lect. Notes Comput. Sci. 286, 144-150 (1987; Zbl 0641.90005)], the authors proved that a property of ‘acyclicity’ in fuzzy preference relations was a necessary and sufficient condition for the existence of unfuzzy nondominated alternatives when such a set of alternatives is finite. In this paper, a general property of ‘foundation’ is proved to be a necessary and sufficient condition, without requiring finiteness on the set of alternatives. Both concepts are based on classical results in crisp binary relations.

91B08 Individual preferences
Full Text: DOI
[1] Montero, F.J.; Tejada, J., Some problems on the definition of fuzzy preference relations, Fuzzy sets and systems, 20, 45-53, (1986) · Zbl 0601.90005
[2] Montero, F.J.; Tejada, J., Fuzzy preferences in decision-making, () · Zbl 0641.90005
[3] Orlovsky, S.A., Decision-making with fuzzy preference relations, Fuzzy sets and systems, 1, 155-167, (1978) · Zbl 0396.90004
[4] Pattanaik, P.K., Voting and collective choice, (1971), Cambridge University Press London
[5] Sen, A.K., Collective choice and social welfare, (1970), Holden-Day San Francisco, CA · Zbl 0227.90011
[6] Zadeh, Z.A., Similarity relations and fuzzy orderings, Inform. sci., 3, 177-200, (1971) · Zbl 0218.02058
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