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ON FUZZY k−IDEALS, k−FUZZY IDEALS AND FUZZY 2−PRIME IDEALS IN Γ−SEMIRINGS
Murali Krishna Rao, M.,Venkateswarlu, B. The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
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<sub>μ</sub> is a 2-prime ideal of Γ-semiring M if and only if μ is a fuzzy prime ideal of Γ-semiring M.
Tripolar fuzzy interior ideals and tripolar fuzzy soft interior ideals over semigroups
Marapureddy Murali Krishna Rao 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.3
M.Murali Krishna Rao [14] introduced the notion of tripolar fuzzy set as a generalization of fuzzy set, bipolar fuzzy set and intuitionistic fuzzy set.The tripolar fuzzy set representation is very useful in discriminating relevant elements, irrelevent elements and contrary elements. In this paper,we introduce the notion of tripolar fuzzy interior ideal,tripolar fuzzy soft ideal, tripolar fuzzy soft interior ideal over semigroup and study some of their algebraic properties.
On fuzzy $k-$ideals, $k-$fuzzy ideals and fuzzy $2-$prime ideals in $\Gamma -$semirings
M. Murali Krishna Rao,B. Venkateswarlu 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
The notion of $\Gamma -$semiring was introduced by M. Murali Krishna Rao \cite{8} as a generalization of $\Gamma -$ring as well as of semiring. In this paper fuzzy $k-$ideals, $k-$fuzzy ideals and fuzzy-$2-$prime ideals in $\Gamma -$semirings have been introduced and study the properties related to them. Let $\mu$ be a fuzzy $k-$ideal of $\Gamma -$semiring $M$ with $| Im(\mu)| =2$ and $\mu(0)=1.$ Then we establish that $M_{\mu}$ is a $2-$prime ideal of $\Gamma -$semiring $M$ if and only if $\mu$ is a fuzzy prime ideal of $\Gamma -$semiring $M.$
Bi-interior ideals and Fuzzy bi-interior ideals of Γ-semigroups
Marapureddy Murali Krishna Rao 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.24 No.1
In this paper, we introduce the notion of a bi-interior ideal, fuzzy bi-interior ideal of Γ-semigroup and study the properties of bi-interior ideals, minimal bi-interior ideal and fuzzy bi-interior ideal. We characterize the (fuzzy)bi-interior ideal of Γ-semigroup and regular Γ-semigroup in terms of (fuzzy) bi-interior ideal of Γ-semigroup.
Tri-ideals and fuzzy tri-ideals of $\Gamma$-semirings
M. Murali Krishna Rao 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.18 No.2
In this paper, we introduce the notion of tri-ideal and fuzzy tri-ideal of $\Gamma$-semirings, characterize the regular $\Gamma$-semiring in terms of fuzzy tri-ideals of $\Gamma$-semiring and study some of their properties.
A study of a translational invariant fuzzy subset of a semigroup
M. Murali Krishna Rao 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.25 No.2
The purpose of this paper is to introduce the notion of left and right translational invariant fuzzy subset of a semigroup and the notion of a unit with respect to fuzzy subset of a semigroup and study their properties. We prove that if $\mu$ is a translational invariant fuzzy subset of a commutative semigroup with unity then principal ideal generated by an element and fuzzy subset is a prime ideal of a semigroup.
Fuzzy soft quasi-interior ideals of Γ-semirings
M. Murali Krishna Rao 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.22 No.3
In this paper, we introduce the notion of quasi-interior ideal and fuzzy soft quasi-interior ideal of $\Gamma$-semiring and we characterize the regular $\Gamma$-semiring in terms of fuzzy soft quasi-interior ideal of $\Gamma$-semiring.
Fuzzy tri-ideals and fuzzy soft tri-ideals over semirings
Marapureddy Murali Krishna Rao,Rajendra Kumar Kona 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.24 No.3
In this paper, we introduce the notion of fuzzy tri-ideal, fuzzy soft tri-ideal over semirings and study some of their properties. Every fuzzy soft left (right) ideal over semiring is a fuzzy soft right (left) tri- ideal over semiring. We characterize the regular semiring in terms of fuzzy left ( right) tri ideals and fuzzy soft left ( right) tri-ideals over semiring.
T-fuzzy ideals in ordered Γ-semirings
Marapureddy Murali Krishna Rao 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.13 No.2
In this paper,we introduce the notion of $T-$fuzzy ideal, $T-$fuzzy left (right) $k-$ideal, $T-$fuzzy interior ideal, $T-$fuzzy quasi ideal, $T-$fuzzy bi-ideal in an ordered $\Gamma-$semiring. We characterize the regular ordered $\Gamma-$semiring in terms of $T-$fuzzy left (right) ideal, $T-$fuzzy quasi ideal, $T-$fuzzy bi-ideal, $T-$fuzzy interior ideal and study their properties and relations between them. We establish that $T-$fuzzy ideal, $T-$fuzzy bi-ideal, $T-$fuzzy quasi ideal and $T-$fuzzy interior ideal are equivalent in a regular ordered $\Gamma -$semiring and characterize the simple ordered $\Gamma -$semiring in terms of $T-$fuzzy interior ideal.
Tripolar fuzzy interior ideals of Γ-semigroup
M. Murali Krishna Rao 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.2
In this paper, we introduce the notion of tripolar fuzzy set to be able to deal with tripolar information as a generalization of fuzzy set, bipolar fuzzy set and intuitionistic fuzzy set.The tripolar fuzzy set representation is very useful in discriminating relevant elements, irrelevent elements and contrary elements.We introduce the notion of tripolar fuzzy interior ideal of $\Gamma -$ semigroup and study some of their algebraic properties.