A new class of hypergroupoids, deriving from binary relations, is presented, via the introduced path hyperoperation. Its properties are investigated and its connections with Graph Theory are also delineated. Moreover, we present an application of this hyperoperation to assembly line designing and management.

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.

the aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. in thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle htimes h, otimesrangle$ in a particularcase.

The aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. In thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle Htimes H, otimesrangle$ in a particularcase.

Every binary relation ρ on a set H, (card(H) > 1) can define a hypercomposition and thus endow H with a hypercompositional structure. In this paper the binary relations are represented by Boolean matrices. With their help, the hypercompositional structures (hypergroupoids, hypergroups, join hypergroups) that derive with the use of the Rosenberg’s hyperoperation, are characterized, constructed a...

In recitals of this paper there we will be repeated the definitions and main results mentioned 1n [15] without proofs. The definition of the multioperation on partially ordered carrier set in this papers is idempotent, commutative but not associative operation. In the opening part of this article there we repeat fundamental definitions and some theorems without proofs. In the next part of this ...

In this work we introduce the concept of Atanassov’s intuitionistic fuzzy index of a hypergroupoid based on the notion of intuitionistic fuzzy grade of a hypergroupoid. We calculate it for some particular hypergroups, making evident some of its special properties.

In this work we prove that the set of congruences on an nd-groupoid under suitable conditions is a complete lattice which is a sublattice of the lattice of equivalence relations on the nd-groupoid. The study of these conditions allowed to construct a counterexample to the statement that the set of (fuzzy) congruences on a hypergroupoid is a complete lattice.

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.