A theoretical investigation on different types of intuitionistic fuzzy filter in lattice implication algebra

Abstract

The present research deals with the new types of intuitionistic fuzzy filter in lattice implication algebra. Their characterizations, different properties and their interrelations have been presented. Intuitionistic fuzzy fantastic filter is defined and some of its properties are studied. Equivalent conditions required for an intuitionistic fuzzy filter to become an intuitionistic fuzzy fantastic filter are also obtained. Further intuitionistic fuzzy positive implicative filter is defined and its properties are studied. Every intuitionistic fuzzy positive implicative filter to be an intuitionistic fuzzy fantastic filter is obtained. The concept of intuitionistic fuzzy associative filter is introduced in lattice implication algebra and some of its properties are studied. Additionally, the equivalent conditions needed for an intuitionistic fuzzy filter to be an intuitionistic fuzzy associative filter are obtained. The intuitionistic fuzzy transitive filter in lattice implication algebra and its properties is studied. Further intuitionistic fuzzy absorbent filter in lattice implication algebra are introduced and studied. Finally the concepts of intuitionistic fuzzy n-fold positive implicative filter, intuitionistic fuzzy n-fold fantastic filter, intuitionistic fuzzy n-fold associative filter, intuitionistic fuzzy n-fold transitive filter, intuitionistic fuzzy n-fold absorbent filter in lattice implication algebra are introduced and their interrelations have been presented. newline