A new characterization of the product of (L, M)-fuzzy convex structures1

Abstract

In order to give a characterization of the product of (L, M)-fuzzy convex structures, the notion of convex (L, M)-fuzzy hull operators is presented, it is proved that the category of (L, M)-fuzzy convex structures and the category of convex (L, M)-fuzzy hull operators are isomorphic. In particular, the lattices structure of convex (L, M)-fuzzy hull operators and a new characterization of the product of (L, M)-fuzzy convex structures are given.

Convex (L,M)-fuzzy remote neighborhood operators

“…Actually, both L-convex structures and M -fuzzifying convex structures can be regarded as special cases of (L, M )-fuzzy convex structures (see [12]). At present, many researchers studied fuzzy convex structures from different aspects, such as fuzzy hull operators, fuzzy interval operators, bases and subbases, product and coproduct structures, fuzzy betweenness relations, and so on (see, for example [7,8,12,25,26,27]).…”