Intuitionistic fuzzy filters in Sheffer stroke Hilbert algebras

Abstract

Using the Atanassov's intuitionistic fuzzy set, the concept of intuitionistic fuzzy deductive system and intuitionistic fuzzy filter in Sheffer stroke Hilbert algebras is introduced, several properties are investigated.  The conditions under which an intuitionistic fuzzy set can be an intuitionistic fuzzy filter are explored, and  characterizations of an intuitionistic fuzzy filter are considered.  The process of making an intuitionistic fuzzy filter through the collection of filters is displayed, and the union and intersection of intuitionistic fuzzy filters are discussed. Several properties are investigated in relation to the homomorphsm of Sheffer stroke Hilbert algebras, and finally the relationship between an intuitionistic fuzzy filter and an intuitionistic fuzzy deductive system is established.