• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.141-148
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• 2006

Fuzzy (weak) implicative hyper K-ideals are introduced, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are discussed.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.531-542
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• 2011

The notion of bipolar fuzzy a-ideals of BCI-algebras is introduced, and their properties are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals and bipolar fuzzy a-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy a-ideal are provided. Characterizations of bipolar fuzzy a-ideals are given. Using a finite collection of a-ideals, a bipolar fuzzy a-ideal is established.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.259-268
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• 2007

The notion of intuitionistic fuzzy Lie ideal of a Lie algebra is introduced, and related properties are investigated. Characterizations of an intuitionistic fuzzy Lie ideal are provided. Using a collection of Lie ideals, an intuitionistic fuzzy Lie ideal is established.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.453-465
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• 2013

The notion of vague $p$-ideals and vague $a$-ideals of BCI-algebras is introduced, and several properties of them are investigated. We show that a vague set of a BCI-algebra is a vague $a$-ideal if and only if it is both a vague $q$-ideal and a vague $p$-ideal.

• 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.

• 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.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.435-457
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• 2013

Using the Lukasiewicz 3-valued implication operator, the notion of an (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring is introduced, where ${\alpha},{\beta}{\in}\{{\in},q,{\in}{\wedge}q,{\in}{\vee}q\}$. We define intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) and (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$)-intuitionistic fuzzy left (right) $h$-ideal of R if and only if A is an intuitionistic fuzzy left (right) $h$-ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$))-intuitionistic fuzzy left (right) $h$-ideal if and only if for any $p{\in}$ (0, 1] (or $p{\in}$ (0, 0.5] or $p{\in}$ (0.5, 1] ), $A_p$ is a fuzzy left (right) $h$-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of R if and only if for any $p{\in}(s,t]$, the cut set $A_p$ is a fuzzy left (right) $h$-ideal of R.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.199-204
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• 1997

To develope the theory of BCI-algebras, the idel theory plays an important role. The first author [4] introduced the notion of T-ideal in BCI-algebras. In this paper, we first construct a special set, called T-part, in a BCI-algebra X. We show that the T-part of X is a subalgebra of X. We give equivalent conditions that the T-part of X is an ideal. By using T-part, we provide an equivalent condition that every ideal is a T-ideal.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.1-15
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• 2010

We introduce, in this article, the quasi-stable exchange ideal for associative rings. If I is a quasi-stable exchange ideal of a ring R, then so is $M_n$(I) as an ideal of $M_n$(R). As an application, we prove that every square regular matrix over quasi-stable exchange ideal admits a diagonal reduction by quasi invertible matrices. Examples of such ideals are given as well.

• Fashion & Textile Research Journal
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• v.14 no.3
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• pp.371-380
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• 2012

Based on results using factor analysis, Women's definition of "Ideal beauty" can be materialize into four key factors, "Confident beauty", "Graceful beauty", "Lively beauty", and "Genuine beauty". Factor analysis was conducted to materialize Women's definition of "Ideal beauty"and the above four factors were representative of 56.31% of total variance. "Ideal beauty" defined by age category was also found significant difference, indicating existence of different "Ideal beauty "definition for age groups. Itemized age category's "Ideal beauty" definitions are as follows, 18-22 years, bright and lively, 23-27 years, cute and confident, 28-32 years, sensible and confident 33-37 years, hard-working, 38-42 years, ability and composure, 43-47 years, casual and graceful, 48-52 years, refined and noble, 53 years and above, healthy and proper as "Ideal beauty" definitions. The defined "ideal beauty" was steadily shifted with age group. Women 38 years and younger were defined external attributes to "Ideal beauty", as women 38 years and older were defined inner attributes to "Ideal beauty". Women's definition of "Ideal beauty" can materialize into four key factors, "Confident beauty", "Graceful beauty", "Lively beauty", and "Genuine beauty".