An Overview of Fuzzy Quanti ers Part Interpretations

Quanti cation is an important topic in fuzzy theory and its applica tions An overview is presented for quanti cation in fuzzy theory After This work has been supported by the International Projects of the Flemish Community Cooperation with P R China No a brief review of quanti ers in rst order logic two approaches of gen eralizing quantifers are given the algebraic method and the substitution method By distinguishing the fuzziness of predicates and quanti ers var ious approaches to quanti cation in fuzzy logic can be organized Quanti ers in rst order logic can be generalized in crisp sense and these gener alized quanti ers can also be applied to fuzzy sets Moreover quanti ers themselves can be fuzzy i e they can only be represented by a fuzzy set These di erent kinds of quanti cations are identi ed Quanti ers relate close to the concept of the cardinality of a fuzzy set which is summarized before investigating fuzzy quanti cations Di erent to classical logic var ious semantics of propositions in fuzzy logic fall into di erent frameworks which are known as the possibility distribution based reasoning system and the many valued fuzzy logics Accordingly numerical and possibilis tic interpretation explored in literature are reviewed conforming to these two frameworks