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Transitive decomposition of fuzzy preference relations: The case of nilpotent minimum. (English) Zbl 1249.91024

Summary: Transitivity is a fundamental notion in preference modelling. In this work, we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum \(t\)-norm and decompose it into an indifference and strict preference relation by means of generators based on \(t\)-norms, i.e., using a Frank \(t\)-norm as indifference generator. We identify the strongest type of transitivity these indifference and strict preference components show, both in general and for the important class of weakly complete large preference relations.

MSC:

91B08 Individual preferences
06F05 Ordered semigroups and monoids
03E72 Theory of fuzzy sets, etc.
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