Deductive systems and filters of Sheffer stroke Hilbert algebras based on the bipolar-valued fuzzy set environment

Abstract

The notion of bipolar-valued fuzzy set is used to treat the filter and deductive system in Sheffer stroke Hilbert algebras. The concepts of bipolar valued fuzzy filter and bipolar-valued fuzzy deductive system are introduced and related properties are investigated. Conditions under which the bipolar-valued fuzzy set can be a bipolar-valued fuzzy filter are explored. Characterizations of the bipolar-valued fuzzy filter are examined. A bipolar-valued fuzzy filter is built using a filter. To consider the nomality of bipolar-valued fuzzy filter, the notion of normal bipolar-valued fuzzy filter is introduced and related properties are investigated. The method of normalizing the bipolar-valued fuzzy filter is addressed, and we will see what the normal bipolar-valued fuzzy filter looks like.