Filter Theory in Pre-ordered Residuated Systems Using Intuitionistic Fuzzy Points

Using the notion of intuitionistic fuzzy points, the concept of intuitionistic fuzzy filters and [Formula: see text]-intuitionistic fuzzy filters in pre-ordered residuated systems are introduced, and several related properties are investigated. Characterizations of intuitionistic fuzzy filters and [Formula: see text]-intuitionistic fuzzy filters are studied. By forming sub-structures called intuitionistic level set, intuitionistic [Formula: see text]-set, intuitionistic [Formula: see text]-set, and [Formula: see text]-set, the conditions under which they can be filters will be tracked.