A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in (Fuzzy Sets Syst., 117: 477– 484, 2001) and Bhakat and Das in (Fuzzy Sets Syst., 80: 359–368, 1996). The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued (α, β)-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued (α, β)-fuzzy sub-hypermodule is a generalization of the usual fuzzy sub-hypermodule. We shall study such fuzzy sub-hypermodules and consider the implication-based interval-valued fuzzy sub-hypermodules of a hypermodule.