on a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. in this paper we extend thisconcepts to the fuzzy case. we give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

In this paper we start with a lattice (X,∨,∧) and define, in terms of ∨, a family of crisp hyperoperations tp (one hyperoperation for each p ∈ X). We show that, for every p, the hyperalgebra (X,tp) is a join space and the hyperalgebra (X,tp,∧) is very similar to a hyperlattice. Then we use the hyperoperations tp as p-cuts to introduce an L-fuzzy hyperoperation t and show that (X,t) is an L-fuzz...

In this paper we study the L-fuzzy hyperoperation t, which generalizes the crisp Nakano hyperoperation t1. We construct t using a family of crisp tp hyperoperations as its p-cuts. The hyperalgebra (X,t,∧) can be understood as an L-fuzzy hyperlattice. AMS Classification: 06B99, 06D30, 08A72, 03E72, 20N20.

On a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. In this paper we extend thisconcepts to the fuzzy case. We give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

In this paper we study relations which are congruences with respect to ∧ and ⊔p, where ⊔pis the p-cut of the L-fuzzy hyperoperation ⊔. The main idea is to start from an equivalence relation R1 which is a congruence with respect to ∧ and ⊔1and, for each p ∈ X , construct an equivalence relation Rp which is a congruence with respect to ∧ and ⊔p. Furthermore, for each x ∈ Rp we construct a quotien...

We introduced and study fuzzy Γ-hypersemigroups, according to fuzzy semihypergroups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy Γ-hypersemigroup. We will proceed by study fuzzy Γ-hyperideals and fuzzy Γ-bihyperideals. Also we study the relation between the classes of fuzzy Γ-hypersemigroups and Γ-...

This paper is the results of the ideas suggested by P. Corsini in his paper [10]. Our investigations take in account the paper [13] of I. Cristea. We study the hypergroup generated by the cosets modulo a subgroup (normal subgroup). We prove that (G/H, ◦4) is a complete hypergroup. We take many particular examples to illustrate some known results on hypergroups. Keyword: fuzzy sets, hypergroups,...

in a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. indeed, the notion of ternary semihyperringsis a generalization of semirings. our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.we give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.

In a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. Indeed, the notion of ternary semihyperringsis a generalization of semirings. Our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.We give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.