Equivalence and compositions of fuzzy rationality measures

An axiomatic basis for fuzzy rationality measures has already been introduced by the authors in a previous paper [5], formalizing the fact that there exist degrees of consistency when preferences over a fixed set of alternatives are expressed in terms of fuzzy binary preference relations. This paper deals with some practical consequences. On the one hand, similarities and compositions of fuzzy rationality measures are considered, showing natural ways of deriving new measures; on the other, if basic stability properties are introduced in order to assure that small intensity measurement errors never lead to big changes in the associate rationality value, it is shown that crisp (i.e., binary) rationality measures present serious difficulties when applied to fuzzy preference relations.

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