Penta-Valued Fuzzy Set

Abstract

This paper presents an extension of fuzzy set based on Lukasiewicz penta-valued logic. This new type of fuzzy set will be called penta-valued fuzzy set and will be defined by five scalar functions: the strong membership, the weak membership, the uncertainty, the weak non-membership and the strong non-membership. Also, the penta-valued fuzzy set represents an extension for the intuitionistic fuzzy sets and for the four-valued fuzzy set.