EQUIVALENCE AND COMPOSITIONS OF FUZZY RATIONALITY MEASURES

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