Picture fuzzy filters on residuated lattices

Filters play an important role in studying fuzzy logics. From a logical point of view, filters correspond to sets of provable formulae. In this paper, the concept of picture fuzzy sets is applied to residuated lattices. The notion of picture fuzzy filters of a residuated lattice is introduced and some related properties are investigated. The characterizations of picture fuzzy filters are obtained. We show that the set of all the picture fuzzy filters of a residuated lattice forms a distributive lattice. Finally, a unified approach to picture fuzzy filter is proposed and the simple general principles of picture fuzzy filters are given. The relationships between various picture fuzzy filters are studied, by means of the quotient they determine.