ON (L;M)-FUZZY CLOSURE SPACES

Abstract. The aim of this paper is to introduce (L,M)-fuzzy closure structure where L and M are strictly two-sided, commutative quantales. Firstly, we define (L,M)-fuzzy closure spaces and get some relations between (L,M)- double fuzzy topological spaces and (L,M)-fuzzy closure spaces. Then, we introduce initial (L,M)-fuzzy closure structures and we prove that the category (L,M)-FC of (L,M)-fuzzy closure spaces and (L,M)-C-maps is a topological category over the category SET. From this fact, we define products of (L,M)-fuzzy closure spaces. Finally, we show that an initial structure of (L,M)-double fuzzy topological spaces can be obtained by the initial structure of (L,M)-fuzzy closure spaces induced by those.