A New View on Fuzzy Hypermodules

The L-fuzzy hypermodules

“…This approach can be extended to fuzzy hypergroups. For example, given a crisp hypergroup (H, •) and a fuzzy subset µ in H, then we say that µ is a fuzzy subhypergroup of H if every cut set of µ say µ t , is a (crisp) subhypergroup of H. This was initiated by Zahedi et al [13] and continued by Ameri and Hedayati [14], Davvaz and Corsini [15], Davvaz et al [16], Zhan et al [17][18][19][20][21] and so on. The third approach involves the definition and study of fuzzy hyperoperations.…”

The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets

“…Then, this concept has been studied by a variety of authors. Various hypermodules have been studied by several authors, for example, Massouros [31], Vougiouklis [49], Davvaz [10,11], Zhan et al [59] and Ameri [1]. The fuzzy isomorphism theorems of hypermodules are given [58].…”

Isomorphism theorems of fuzzy hypermodules

“…The second approach consists in defining a fuzzy subset on crisp hyperstructures and was introduced by Zahedi et al [30]. Some interesting papers in this direction are [9], [15], [16], [31], and [32]. Finally, the third group of papers on fuzzy hyperstructures associates a fuzzy set with each pair of elements of a set.…”