applications of hypergroups have mainly appeared in special subclasses. one of the important subclasses is the class of polygroups. in this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. in particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

Applications of hypergroups have mainly appeared in special subclasses. One of the important subclasses is the class of polygroups. In this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. In particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

This paper concerns a relationship between soft sets and n-ary polygroups. We consider the notion of an n-ary polygroup as a generalization of a polygroup and apply the notion of soft sets to n-ary polygroups. Some related notions are defined and several basic properties are discussed by using the soft set theory. Furthermore, we propose the homomorphism of n-ary polygroups and investigate the ...

in this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of loday's definition‎. ‎then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

Linear Diophantine fuzzy sets were recently introduced as a generalized form of sets. The aim this paper is to shed the light on relationship between algebraic hyperstructures and linear through polygroups. More precisely, we introduce concepts subpolygroups polygroup, normal anti-fuzzy polygroup. Furthermore, study some their properties characterize them in relation level ceiling

In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

In this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of Loday's definition‎. ‎Then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎Specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

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.