This paper deals with hypergroupoids obtained from n-ary relations. We give conditions for an n-ary relation such that the hypergroupoid associated with it is a hypergroup. First we analyze this construction using a ternary relation and then we generalize it for an n-ary relation.

measure always exists on a commutative hypergroup K, and there always exists a 'Plancherel measure' on the dual space K of equivalence classes of irreducible representations of K, with respect to which Plancherel's formula holds for Fourier transforms. In contrast with the case of a locally compact abelian group, however, the Plancherel measure is not necessarily a Haar measure on K, and K need...

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

We generalize the concept of topological hypergroup to Hv-group and define some topologies on Hv-groups by using geometric space, which was defined Freni. By applying these topologies, we have always a without need any more conditions. Moreover, state conditions that make it complete. Our aim is via considering characteristics induced space.

We introduce and study the construction of commutative fundamental relation in fuzzy hypersemigroups and investigate its basic properties. We will determine some necessary and sufficient conditions so that this relation is transitive in fuzzy hypersemigroups. Also we show that this relation is transitive in every fuzzy hypergroup.