In this paper, a special class of rings for which an element a in R, satisfying the additional pr... more In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.
The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain so... more The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain some characterizations.
In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum... more In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum of anti fuzzy ideals of a Γ-near-ring. 2010 AMS Classification: 16Y30, 03E72
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of... more In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of -near-rings is introduced. Homomorphism and endomorphism of interval-valued anti fuzzy ideal in -near-rings is discussed. Also union of interval valued -near rings, image and pre-image of interval valued -near-rings with respect to anti fuzzy ideals are studied. AMS subject classification: 16Y30, 03E72.
The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ide... more The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ideal of a POGN(TFKIPOGN), quotient POGN, and normal TFKIPOGN are introduced and investigated the basic properties. I also propose some necessary sufficient conditions on POGN under the T-norm.
In this paper we establish the few relations on cen tral loops and we investigate the central loo... more In this paper we establish the few relations on cen tral loops and we investigate the central loops are power associative. The commut ative left central loops if and only if they are right central loops. We also establish the central loops representation is alternative and flexible. Andrew Rajah and Chong K am Yoon are proved the construction of M (G, 2), the Moufang loops are isomorphic to M (G, 2). It is an important note that we are extended the previous work Andrew Rajah (11) , the Central loops are isomorphic to C (G, 2) .
The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-... more The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-ideal of PON and fuzzy magnified translation have been proposed in this paper. Characterization of partially ordered near-ring in terms of fuzzy ideals has been obtained.
In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzz... more In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzzy bi-ideals and the characteristic function of fuzzy ideals in PO-G-semigroups. Also we proved the equivalent statements, necessary and suf cient conditions on partial ordered Gsemigroups.
... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ =... more ... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ = (ii) Let x, y, z∈M and Γ ∈ β α, then we have ( ) ) (zyxf zyxA i i β α β α Λ = I = { } Mzx izfxf i i ∈ Λ ∈ , /)( inf { } { } { Mz izf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf, , /)( inf { } )( , zf xf Max i i Λ Λ = ...
Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set t... more Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set theory. Then notions of soft h-hemiregular hemirings, soft h-intra-hemiregular hemirings and soft h-semisimple hemirings are introduced and some properties of them are ...
RECENT TRENDS IN PURE AND APPLIED MATHEMATICS, 2019
In this research article, we introduce the notion of sum and direct sum of vague ideals of a near... more In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring ... more In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring and also discuss some related properties of vague ideals of gamma near-ring.
In this paper, a special class of rings for which an element a in R, satisfying the additional pr... more In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.
The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain so... more The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain some characterizations.
In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum... more In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum of anti fuzzy ideals of a Γ-near-ring. 2010 AMS Classification: 16Y30, 03E72
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of... more In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of -near-rings is introduced. Homomorphism and endomorphism of interval-valued anti fuzzy ideal in -near-rings is discussed. Also union of interval valued -near rings, image and pre-image of interval valued -near-rings with respect to anti fuzzy ideals are studied. AMS subject classification: 16Y30, 03E72.
The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ide... more The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ideal of a POGN(TFKIPOGN), quotient POGN, and normal TFKIPOGN are introduced and investigated the basic properties. I also propose some necessary sufficient conditions on POGN under the T-norm.
In this paper we establish the few relations on cen tral loops and we investigate the central loo... more In this paper we establish the few relations on cen tral loops and we investigate the central loops are power associative. The commut ative left central loops if and only if they are right central loops. We also establish the central loops representation is alternative and flexible. Andrew Rajah and Chong K am Yoon are proved the construction of M (G, 2), the Moufang loops are isomorphic to M (G, 2). It is an important note that we are extended the previous work Andrew Rajah (11) , the Central loops are isomorphic to C (G, 2) .
The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-... more The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-ideal of PON and fuzzy magnified translation have been proposed in this paper. Characterization of partially ordered near-ring in terms of fuzzy ideals has been obtained.
In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzz... more In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzzy bi-ideals and the characteristic function of fuzzy ideals in PO-G-semigroups. Also we proved the equivalent statements, necessary and suf cient conditions on partial ordered Gsemigroups.
... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ =... more ... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ = (ii) Let x, y, z∈M and Γ ∈ β α, then we have ( ) ) (zyxf zyxA i i β α β α Λ = I = { } Mzx izfxf i i ∈ Λ ∈ , /)( inf { } { } { Mz izf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf, , /)( inf { } )( , zf xf Max i i Λ Λ = ...
Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set t... more Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set theory. Then notions of soft h-hemiregular hemirings, soft h-intra-hemiregular hemirings and soft h-semisimple hemirings are introduced and some properties of them are ...
RECENT TRENDS IN PURE AND APPLIED MATHEMATICS, 2019
In this research article, we introduce the notion of sum and direct sum of vague ideals of a near... more In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring ... more In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring and also discuss some related properties of vague ideals of gamma near-ring.
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