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Transitive fuzzy orderings of fuzzy numbers. (English) Zbl 0675.06002
In this well-organized paper a generalization of the Baas-Kwakernaak index [S. M. Baas and H. Kwakernaak, Automatica 13, 47-58 (1977; Zbl 0363.90010)] is presented by replacing the min operation in their definition by a t-norm. Essential properties of the thus defined induced fuzzy ordering are established. Moreover, it is shown that there are classes of fuzzy numbers such that this index defines transitive fuzzy ordering of fuzzy numbers in these classes. The obtained results are illustrated by examples.
Reviewer: J.Albrycht

MSC:
06A99 Ordered sets
91B06 Decision theory
03E72 Theory of fuzzy sets, etc.
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