Filter Theory in Pre-Ordered Residuated Systems using Intuitionistic Fuzzy Points

Abstract

Using the notion of intuitionistic fuzzy points, the concept of intuitionistic fuzzy filters and (is an element of,is an element of boolean OR q)-intuitionistic fuzzy filters in pre-ordered residuated systems are introduced, and several related properties are investigated. Characterizations of intuitionistic fuzzy filters and (is an element of,is an element of boolean OR q)-intuitionistic fuzzy filters are studied. By forming sub-structures called intuitionistic level set, intuitionistic q-set, intuitionistic is an element of boolean OR q-set, and (0, 1)-set, the conditions under which they can be filters will be tracked.