In this paper it has been studied the sequence of membership functions and of join spaces (see [7]), determined by a class of 1–hypergroups which are not complete (see [2]).

One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${bf Z}/n {bf Z},$ calculating their fuzzy grades.

one studies the $hx$-hypergroups, corresponding to the chinese hypergroups associated with the direct products of some ${bf z}/n {bf z},$ calculating their fuzzy grades.

We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthog...