• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.395-404
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• 2020

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of fuzzy (K, ε)-subalgebras, fuzzy (K, ε)-ideals and fuzzy commutative (K, ε)-ideals are introduced, and their relations/properties are investigated. Conditions for a fuzzy subalgebra/ideal to be a fuzzy (K, ε)-subalgebra/ideal are provided.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.193-209
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• 2005

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

• East Asian mathematical journal
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• v.23 no.1
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• pp.23-36
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• 2007

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.321-330
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• 2006

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.353-367
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• 2005

Some properties of the intuitionistic fuzzy (1, 2)-ideal is considered. Characterizations of an intuitionistic fuzzy (1, 2)-ideal are given. We show that every intuitionistic fuzzy (1, 2)-ideal in a group is constant. Using a chain of (1, 2)-ideals of a semigroup S, an intuitionistic fuzzy (1, 2)-ideal of S is established.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.2
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• pp.115-119
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• 2007

The notion of ideals in subtraction algebras and characterizations of ideals introduced by Y.B.Jun et al. [?]. Using this idea, we consider the fuzzification of an ideal of a subtraction algebra. In this paper, we define the concept of a fuzzy ideal of a subtraction algebra and study characterizations of a fuzzy ideal. We give some conditions to show that a fuzzy set in a subtraction algebra is a fuzzy ideal of a subtraction algebra. We investigate the generalization of some properties of a fuzzy ideal of a subtraction algebra.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.255-263
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• 2003

Fuzzifications of n-fold quasi-associative ideals are considered. Conditions for a fuzzy ideal to be a fuzzy n-fold quasi-associative ideal are given. Using a collection of n-fold quasi-associative ideals, fuzzy n-fold quasi-associative ideals are constructed. Finally, the extension property for fuzzy n-fold quasi-associative ideals is established.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.405-419
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• 2016

The notion of Γ-semiring was introduced by M. Murali Krishna Rao [8] as a generalization of Γ-ring as well as of semiring. In this paper fuzzy k-ideals, k-fuzzy ideals and fuzzy-2-prime ideals in Γ-semirings have been introduced and study the properties related to them. Let μ be a fuzzy k-ideal of Γ-semiring M with |Im(μ)| = 2 and μ(0) = 1. Then we establish that M_μ is a 2-prime ideal of Γ-semiring M if and only if μ is a fuzzy prime ideal of Γ-semiring M.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.83-93
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• 2009

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy $\alpha$-I-open and r-fuzzy $\beta$-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy $\alpha$-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal $\alpha$-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.