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

in this paper using strongly duplexes we introduce a new class of (semi)hypergroups. the associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. two computer programs written in matlab show that the two groups $z_{2n}$ and $z_{n}times z_{2}$ produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.

In this paper we introduce fuzzy congruence and fuzzy strong congruence of semi-hypergroups as well as polygroups. We obtain some results in this respect. We also prove that FC(H), the set of all fuzzy strong congruences on a polygroup H , consists a complete lattice and this lattice is isomorphic to FN (H), the lattice of fuzzy normal subpolygroups.

The objective of this paper is to introduce the concept of neutrosophic hypergroup and present some of its elementary properties.

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them. 2010 AMS Classification: 03B60, 20A05, 20N20, 97H40

In this paper we study random walks on the hypergroup of conics in finite fields. We investigate the behavior of random walks on this hypergroup, the equilibrium distribution and the mixing times. We use the coupling method to show that the mixing time of random walks on hypergroup of conics is only linear. Mathematics Subject Classifications: 60D05, 11A99. Keywoords: random walks, hypergroups,...