• Honam Mathematical Journal
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• v.40 no.1
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• pp.109-124
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• 2018

In this paper, structure of involution ${\Gamma}$-semihypergroup is introduced and some theorems about this concept are stated and proved. The concept of ${\Gamma}$-hyperideal in involution ${\Gamma}$-semihypergroup is defined and some of their properties are studied. Some results on regular ${\Gamma}^*$-semihypergroups and fuzzy ${\Gamma}^*$-semihypergroups are also provided.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.753-774
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• 2020

We introduce the notion of interval valued intuitionistic fuzzy hyperideals, bi-hyperideals and quasi-hyperideals of an ordered semihypergroup. We characterize an interval valued intuitionistic fuzzy hyperideal of an ordered semihypergroup in terms of its level subset. Moreover, we show that interval valued intuitionistic fuzzy bi-hyperideals and quasi-hyperideals coincide only in a particular class of ordered semihypergroups. Finally, we show that every interval valued intuitionistic fuzzy quasi-hyperideal is the intersection of an interval valued intuitionistic fuzzy left hyperideal and an interval valued intuitionistic fuzzy right hyperideal.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1021-1031
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• 1999

In this paper we introduce matrix representations of polygroups over hyperrings and show such representations induce representations of the fundamental group over the corresponding fundamental ring. We also introduce the notion of a polygroup hyperring generalizing the notion of a group ring. We establish homo-morphisms among various polygroup hyperrings.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.205-213
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• 2000

In this paper we introduce the concept of a fuzzy strongly regular relation on a sumihypergroup, and prove a few results concerning this concept.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.233-245
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• 2019

Cyclic hypergroups are of great importance due to their applications to many field in mathematics. In this paper, we classify all polygroups of order less than six where each of its non-identity elements is a generator.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.203-218
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• 2018

An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.93-108
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• 2018

In this paper, we introduce the notion of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals of ${\Gamma}$-semihypergroups by a new approach called soft intersection (briefly, S. I.). It is proved that in regular ${\Gamma}$-semihypergroups the ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and the ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals coincide. Further, we introduce the concept of ($\xi$, ${\zeta}$)-soft simple ${\Gamma}$-semihypergroup and characterize the simple ${\Gamma}$-semihypergroups in terms of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals.