• Korean Journal of Mathematics
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• v.19 no.3
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• pp.321-330
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• 2011

We characterize the fuzzy bi-ideal generated by a fuzzy subset in a semigroup and the fuzzy bi-ideal generated by a fuzzy subset A such that $A{\subseteq}A^2$ in a semigroup with an identity element. Our work generalizes the characterization of fuzzy bi-ideals by Mo and Wang ([8]).

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.367-381
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• 2014

The notion of ${\Gamma}$-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a ${\Gamma}$-semigroup but a ${\Gamma}$-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered ${\Gamma}$-semigroups.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.133-154
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• 2023

In this paper, we introduce the concept of tripolar fuzzy sub-semigroups, tripolar fuzzy ideals, tripolar fuzzy quasi-ideals, and tripolar fuzzy bi-ideals of an ordered semigroup and study some algebraic properties of them. Moreover, we prove that tripolar fuzzy bi-ideals and quasi-ideals coincide only in a particular class of ordered semigroups. Finally, we prove that every tripolar fuzzy quasi-ideal is the intersection of a tripolar fuzzy left and a tripolar fuzzy right ideal.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.531-536
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• 2003

We discuss the roughness of $\Gamma$-subsemigroups and ideals/bi-ideals in $\Gamma$-semigroups.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.359-367
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• 2007

We consider the intuitionistic fuzzification of the concept of several ${\Gamma}$-ideals in a ${\Gamma}$-semigroup S, and investigate some properties of such ${\Gamma}$-ideals.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.341-351
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• 2009

The notion of rough sets was introduced by Z. Pawlak in the year 1982. The notion of a $\Gamma$-semigroup was introduced by M. K. Sen in the year 1981. In 2003, Y. B. Jun studied the roughness of sub$\Gamma$-semigroups, ideals and bi-ideals in i-semigroups. In this paper, we study rough prime ideals and rough fuzzy prime ideals in $\Gamma$-semigroups.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.207-219
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• 2008

We give some properties of intuitionistc fuzzy left, right, and two-sided ideals and bi-ideals of a semigroup. And we characterize a regular semigroup, a semigroup that is a lattice of left(right) simple semigroups, a semigroup that is a semilattice of left(right) groups and a semigroup that is a semilattice of groups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.783-794
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• 2016

The notions of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are introduced, and several properties are investigated. Relations between a hesitant fuzzy left (resp., right) ideal,a hesitant fuzzy bi-ideal and a hesitant fuzzy quasi-ideal are discussed. Characterizations of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are considered.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.603-616
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• 2011

We introduce the concept of an interval-valued fuzzy generalized bi-ideal of a semigroup, which is an extension of the concept of an interval-valued fuzzy bi-ideal (and of a noninterval-valued fuzzy bi-ideal and a noninterval-valued fuzzy ideal of a semi-group), and characterize regular semigroups, and both intraregular and left quasiregular semigroup in terms of interval-valued fuzzy generalized bi-ideals.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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• pp.112-117
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• 2007

The aim of this paper is to characterise regular duo ring R by using the concept of intuitionistic fuzzy left(right,hi,quasi) ideals of R.