• 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.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.173-188
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• 2014

In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.93-108
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• 2018

In this paper, we introduce the notion of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals of ${\Gamma}$-semihypergroups by a new approach called soft intersection (briefly, S. I.). It is proved that in regular ${\Gamma}$-semihypergroups the ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and the ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals coincide. Further, we introduce the concept of ($\xi$, ${\zeta}$)-soft simple ${\Gamma}$-semihypergroup and characterize the simple ${\Gamma}$-semihypergroups in terms of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.411-417
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• 2010

Some characterizations of regular $\Gamma$-rings are described by means of fuzzy ideals. The concepts of fuzzy interior ideals in $\Gamma$-rings and semisimple $\Gamma$-rings are introduced. Some characterizations of semisimple $\Gamma$-rings are investigated by means of fuzzy interior ideals.

• 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.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.307-331
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• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.4
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• pp.262-266
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• 2007

We characterize a fuzzy pairwise $\gamma$-irresolute continuous mapping on a fuzzy bitopological space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.3
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• pp.188-192
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• 2007

We characterize a fuzzy pairwise ${\gamma}-irresolute$ continuous mapping on a fuzzy bitopological space.

• East Asian mathematical journal
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• v.23 no.2
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• pp.213-227
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• 2007

In this paper the concept of fuzzy nearly C-compactness is introduced in Generalized fuzzy topological spaces. Several characterizations and some interesting properties of these spaces in Generalized fuzzy topological spaces are discussed. The properties of fuzzy almost continuous and fuzzy almost open functions in Generalized fuzzy topological spaces are also studied.