• Honam Mathematical Journal
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• v.27 no.4
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• pp.525-541
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• 2005

We give the characterization of an intuitionistic fuzzy ideal[resp. intuitionistic fuzzy left ideal, an intuitionistic fuzzy right ideal and an intuitionistic fuzzy bi-ideal] generated by an intuitionistic fuzzy set in a semigroup without any condition. And we prove that every intuitionistic fuzzy ideal of a semigroup S is the union of a family of intuitionistic fuzzy principle ideals of S. Finally, we investigate the intuitionistic fuzzy ideal generated by an intuitionistic fuzzy set in $S^1$.

• 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.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.99-104
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• 2001

We give the characterization of left(right) semi-regular $po$-semigroups and $Ve$-semigroups.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.492-495
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• 2005

We give the characterization of an intuitionistic fuzzy ideal[resp. intuitionistic fuzzy left ideal, an intuitionistic fuzzy right ideal and an intuitionistic fuzzy hi-ideal] generated by an intuitionistic fuzzy set in a semigroup without any condition. And we prove that every intuitionistic fuzzy ideal of a semigroup S is the union of a family of intuitionistic fuzzy principle ideals of 5. Finally, we investigate the intuitionistic fuzzy ideal generated by an intuitionistic fuzzy set in $S^{1}$

• 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.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.629-638
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• 2014

The concept of prime and weakly prime ideal in semigroups has been introduced by G. Szasz [4]. In this paper, we define the involution in po-${\Gamma}$-semigroups, then we extend some results on prime, semiprime and weakly prime ideals to the involution po-${\Gamma}$-semigroup S. Also, we characterize intra-regular involution po-${\Gamma}$-semigroups. We establish that in the involution po-${\Gamma}$-semigroup S such that the involution preserves the order, an ideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime ideals of S coincide. Finally, we prove that if S is a po-${\Gamma}$-semigroup with order preserving involution, then the ideals of S are prime if and only if S is intra-regular.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.325-331
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• 2008

In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.225-229
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• 2013

According to the paper in [3], the kernel of an ordered semigroup S is a completely regular subsemigroup of S. In this note we show that the kernel of an ordered semigroup S is not a completely regular subsemigroup of S, in general.

• 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.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.139-151
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• 2007

We introduce the concept of intuitionistic fuzzy semiprimality of a semigroup which is an extension of semiprimality in it. And we obtain a characterization of a semigroup that is a semilattice of simple semigroups in terms of intuitionistic fuzzy semiprime interior ideals.