On (L,M)‎-Double Fuzzy Filter Spaces

Abstract EN

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.