Product and coproduct structures of (L, M)-fuzzy hull operators1

Abstract

Notice that there’s a one-to-one correspondence between between (L, M)-fuzzy hull operators and (L, M)-fuzzy convex structures. So, it is necessary to consider the product of (L, M)-fuzzy convex structures through the product structures of (L, M)-fuzzy hull operators. In this paper, we construct the product structures of (L, M)-fuzzy hull operators to characterize the product of (L, M)-fuzzy convex structures. On the other hand, we construct the coproduct structures of (L, M)-fuzzy hull operators to give a reasonable definition with respect to the coproduct of (L, M)-fuzzy convex structures.

Convex (L,M)-fuzzy remote neighborhood operators

“…Remark 2.3. (Zhao et al [25]) The set of all (L, M )-fuzzy convex structrues on X is denoted by FC(X, L, M ). Define a relation ≤ on FC(X, L, M ) as follows:…”

“…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]).…”