A NEW APPROACH TO THE SIMILARITY RELATIONS IN THE FUZZY SET-THEORY

The subtle theory of ''fuzzy'' sets has long been proposed by Zadeh as an extension of the classical theory of ''hard'' sets. In this paper we show how the properties of reflexivity and transitivity of a fuzzy relation may be reconsidered if they are used in view of another intui tive support and new mathematical developments. As a consequence, we p ropose a new modified system of leading definitions for the fuzzy equi valence relationship that could be used profitably to support the conc ept of fuzzy partition. The role of an internal basis is also emphasiz ed. Corollary properties are derived from this new approach.