On (L,M)-Double Fuzzy Filter Spaces

Abstract

We give in this paper the definitions of (L,M)-double fuzzy filter base and (L,M)-double fuzzy filter structures where L and M are strictly two-sided commutative quantales, and we also investigate the relations between them. Moreover, we propose second-order image and preimage operators of (L,M)-double fuzzy filter base and study some of its fundamental properties. Finally, we handle the given structures in the categorical aspect. For instance, we show that the category (L,M)-DFIL of (L,M)-double fuzzy filter spaces and filter maps between these spaces is a topological category over the category SET.

(L,⊙)-Fuzzy (K,E)-Soft Filter

“…The L-filter is a significant tool for investigating the properties of L-fuzzy topological spaces ( [30,31]). L-filter has been developed in different directions ( [32][33][34][35]).…”