Generalized intuitionistic fuzzy filters on residuated lattices

Filters play an important role in studying fuzzy logics. From logical point of view, filters correspond to sets of provable formulae. The aim of this paper is to solve two problems appeared in (alpha, beta]-intuitionistic fuzzy filters of residuated lattices. Some characteristics of (alpha, beta]-intuitionistic fuzzy filters ((alpha, beta]-intuitionistic fuzzy P-filters) are obtained. The relations among (alpha, beta]-intuitionistic fuzzy filters, cut sets and s-upper cut sets are established. The "Extension property" and "Triple of equivalent characteristics" of (alpha, beta]-intuitionistic fuzzy P-filters are also presented.