• 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.

• 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 applied mathematics & informatics
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• v.20 no.1_2
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• pp.255-277
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• 2006

By means of the use of a triangular norm T, the notion of T-fuzzy hyperideals in hypernear-rings is stated, and basic properties are investigated. Moreover, the notion of Noetherian hypernear-rings is introduced, and its characterization is given. At last, the properties of quotient hypernear-rings and T-fuzzy characteristic hyper ideals are discussed.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.31-47
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• 2024

The concept of hybrid structures integrates two powerful mathematical tools: soft sets and fuzzy sets. This paper extends the application of hybrid structures to ordered hypersemigroups. We introduce the notions of hybrid interior hyperideals in ordered hypersemigroups and demonstrate their equivalence with hybrid hyperideals in certain classes, including regular, intra-regular, and semisimple ordered hypersemigroups. Furthermore, we provide a characterization of semisimple ordered hypersemigroups in terms of hybrid interior hyperideals.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.601-610
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• 2018

In the present paper, we construct an ordered regular equivalence relation on an ordered semihyperring by 2-hyperideals such that the corresponding quotient structure is also an ordered semihyperring.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.515-530
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• 2015

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring.