Characterization of fuzzy preference structures through Łukasiewicz triplets (Q1810607)

The author characterizes the reconstruction of a fuzzy set from its subsets by means of Łukasiewicz triplets. This result allows to introduce a new definition of a fuzzy strict preference, which is also satisfied in the crips frameworks. (Subsets of a non-empty set of alternatives \(A\), \(| A|> 2\) will be called crisp subsets of \(A\). A crisp binary relation on \(A\) is a crisp subset of \(A\).) The usual definitions of fuzzy indifference and fuzzy incomparability together with this one enable to construct and to characterize fuzzy preference structures from a reflexive binary relation.