ADVANCES IN FUZZY SYSTEMS, vol.2018, 2018 (ESCI)
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.