• Korean Journal of Mathematics
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• v.28 no.3
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• pp.623-638
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• 2020

In this article, we initially present the concept of the fuzzy generalized m-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized m-bi-ideals, we give the important characterizations of the semigroups. We also characterize the m-regular and m-intraregular semigroups using the properties of the irreducible and strongly irreducible fuzyy generalized m-bi-ideals.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.372-377
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• 2004

We introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a lattice, and discuss the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence on a distributive lattice. Also we prove that for a generalized Boolean algebra, the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences. Finally, we consider the products of intuitionistic fuzzy ideals and obtain a necessary and sufficient condition for an intuitionistic fuzzy ideals on the direct sum of lattices to be representable on a direct sum of intuitionistic fuzzy ideals on each lattice.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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• pp.118-122
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• 2007

In this paper, we consider the intuitionistic fuzzification of the notion of a interior ideal in ordered semigroup S, and investigate some properties of such ideals. In terms of intuitionistic fuzzy set, characterizations of intuitionistic fuzzy interior ideals in ordered semigroups are discussed. Using a collection of interior ideals with additional conditions, an intuitionistic fuzzy interiror ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy interior ideals of an ordered semigroup are investigated. We also give a characterization of a intuitionistic fuzzy simple semigroup in terms of intuitionistic fuzzy interior ideals.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1217-1225
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• 2010

In this paper we define fuzzy interior $\Gamma$-ideals in ordered $\Gamma$-semigroups. We prove that in regular(resp. intra-regular) ordered $\Gamma$-semigroups the concepts of fuzzy interior $\Gamma$-ideals and fuzzy $\Gamma$-ideals coincide. We prove that an ordered $\Gamma$-semigroup is fuzzy simple if and only if every fuzzy interior $\Gamma$-ideal is a constant function. We characterize intra-regular ordered $\Gamma$-semigroups in terms of interior (resp. fuzzy interior) $\Gamma$-ideals.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.198-204
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• 2012

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.11-14
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• 1995

In [1], Alo and Deeba introduced the uniformity of a BCK-algebra by using ideals. Meng [5] introduced the concept of dual ideals in BCK-algebras. We note that the concept of dual ideals is not a dual concept of ideals. In this paper, by using dual ideals, we consider the uniformity of a BCK-algebra.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.41-46
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• 2009

The multiplicative semigroups $\mathbb{Z}_n$ have been widely studied. But, the ideals of $\mathbb{Z}_n$ seem to be unknown. In this paper, we provide a complete descriptions of ideals of the semigroups $\mathbb{Z}_n$ and their product semigroups ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$. We also study the numbers of ideals in such semigroups.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.555-568
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• 2014

On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced. Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCI-commutative ideals are provided. Characterizations of a falling fuzzy BCI-commutative ideal are established, and conditions for a falling fuzzy (closed) ideal to be a falling fuzzy BCI-commutative ideal are considered.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.123-137
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• 2003

In this note first we define the notions of weak implicative and implicative hyper K-ideals of a hyper K-algebra H. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we give some relations between these notions and all types of positive implicative hyper K-ideals. Finally we classify the implicative hyper K-ideals of a hyper K-algebra of order 3.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.585-591
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• 2008

In 1981, Sen [4] have introduced the concept of $\Gamma$-semigroups. We have known that $\Gamma$-semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in $\Gamma$-semigroups and characterize the relationship between the extensions of ideals and some congruences in $\Gamma$-semigroups.