Fuzzy Deductive Systems in Sheffer Stroke Hilbert Algebras

Abstract

With the aim of discussing the deductive system in Sheffer stroke Hilbert algebras using fuzzy sets, the notions of fuzzy deductive system and positive subset in Sheffer stroke Hilbert algebras are introduced, and their properties are investigated. Conditions under which a fuzzy set can be a fuzzy deductive system are explored, and characterizations of a fuzzy deductive system are considered. The situation in which a positive subset will be a deductive system with respect to the conditions that fuzzy sets have is discussed. Also, the situation in which t-level set and -set of a fuzzy set will be deductive systems with respect to the conditions that fuzzy sets have is explored. Finally, fuzzy deductive systems by their level deductive systems are classified.