Parametrization filters and their properties in residuated lattices

Abstract

Filters play a key role in studying algebraic structures of logics. Recently, various special filters in residuated lattices have been introduced. Hence it is very important to develop a general definition for special filters. In the paper, we introduce the notion of parametrization filters and study some of their properties. The relationship of Extension property (Triple of equivalent characteristics, and Quotient characteristics) between the set of parametrization filters and the set of (α, β]-fuzzy parametrization filters is investigated.