• Korean Journal of Mathematics
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• v.13 no.2
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• pp.217-221
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• 2005

Kehayopulu and Tsingelis [2] studied prime ideals of groupoids. Also the author studied prime left (right) ideals of groupoids. In this paper, we give some results on prime bi-ideals of groupoids.

• 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.20 no.1_2
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• pp.455-464
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• 2006

In this paper, we introduce the concept of an interval-valued fuzzy left (right, two-sided, interior, bi-) ideal generated by an interval-valued fuzzy subset in semigroups. Some characterizations of such generated interval-valued fuzzy ideals are also discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.259-266
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• 2011

We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.309-330
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• 2004

In this paper, we apply the concept of intuitionistic fuzzy sets to theory of semigroups. We give some properties of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

• East Asian mathematical journal
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• v.18 no.1
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• pp.155-162
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• 2002

Lajos([1-3]) gave the ideal-theoretical characterizations of some classes of semigroups without "order". The first author([4]) gave the ideal-theoretical characterization of some classes of po-semigroup with order $"{\leq}"$. In this paper we give the other characterizations.

• 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.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.143-154
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• 2015

Characterizations of hesitant fuzzy left (right) ideals are considered. The notion of hesitant fuzzy (generalized) bi-ideals is introduced, and related properties are investigated. Relations between hesitant fuzzy generalized bi-ideals and hesitant fuzzy semigroups are discussed, and characterizations of (hesitant fuzzy) generalized bi-ideals and hesitant fuzzy bi-ideals are considered. Given a hesitant fuzzy set $\mathcal{H}$ on a semigroup S, hesitant fuzzy (generalized) bi-ideals generated by $\mathcal{H}$ are established.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.333-351
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• 2024

In this paper, the concept of Pythagorean fuzzy sets are used to describe in semigroups. Then, some characterizations of regular (resp., intra-regular) semigroups by means of Pythagorean fuzzy left (resp., right) ideals and Pythagorean fuzzy (resp., generalized) bi-ideals of semigroups are investigated. Furthermore, the class of both regular and intra-regular semigroups by the properties of many kinds of their Pythagorean fuzzy ideals also being studied.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.507-511
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• 1997

In this paper, we give the characterizations of right(left) semiregular $po$-semigroups using the notions of some type ideals.