A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism

Rock Arokiaraj; Vellaiyan Saravanan; Jonadoss Jon Arockiaraj

doi:doi:10.11648/j.ajmcm.20210603.12

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A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism

Rock Arokiaraj, Vellaiyan Saravanan, Jonadoss Jon Arockiaraj

Published in American Journal of Mathematical and Computer Modelling (Volume 6, Issue 3)

Received: 3 August 2021 Accepted: 23 August 2021 Published: 4 September 2021

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Abstract

Our motivation in this paper is to start and study the algebraic nature of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. Our purpose of this paper is to initiate and study the notions of (Q,L) - fuzzy normal ℓ-subsemirings of ℓ-semiring.We introduce the concept of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. We study few of their elementary properties by (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring and establish some results on these. These ideas are utilized in the improvement of some significant outcomes. We additionally made an endeavor to study the few properties of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under homomorphism and anti-homomorphism. Also some theorem is the composition operation of functions (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under isomorphism and anti- isomorphism. Also prove some more properties of homomorphism and anti-homomorphism image and pre- image of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring. Finally, we present the theorems of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under image and pre- image of isomorphism and anti- isomorphism.

Published in	American Journal of Mathematical and Computer Modelling (Volume 6, Issue 3)
DOI	10.11648/j.ajmcm.20210603.12
Page(s)	50-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

(Q,L)-fuzzy Subset, (Q,L)-fuzzy ℓ-subsemiring, (Q,L)-fuzzy Normal ℓ-subsemiring, Product of (Q,L)-fuzzy Subsets, Strongest (Q,L)-fuzzy Relation, Pseudo (Q,L)-fuzzy Coset

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[4]	A. Solairaju and R. Nagarajan, A New Structure and Construction of Q-Fuzzy Groups, Advances in fuzzy mathematics, Volume 4, Number 1 (2009), 23-29.
[5]	Biswas. R, Fuzzy subgroups and Anti-fuzzy subgroups, Fuzzy sets and systems, 35, 121-124 (1990).
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[7]	Mohamed Asaad, Groups and fuzzy subgroups, fuzzy sets and systems (1991), North-Holland.
[8]	Palaniappan. N & Arjunan. K, Operation on fuzzy and anti fuzzy ideals, Antartica J. Math., 4 (1) (2007), 59-64.
[9]	Palaniappan, N. and Muthuraj, R., The homomorphism, anti-homomorphism of fuzzy and an anti-fuzzy groups, Varahmihir Journal of Mathematical Sciences, Vol. 4, No. 2 (2004), 387-399.
[10]	Prabir Bhattacharya, Fuzzy Subgroups: Some Characterizations, Journal of Mathematical Analysis and Applications, 128, 241-252 (1987).
[11]	Rajesh Kumar, Fuzzy Algebra, Volume 1, University of Delhi Publication Division, July-1993.
[12]	Salah Abou-Zaid, On generalized characteristic fuzzy subgroups of a finite group, fuzzy sets and systems, 235-241 (1991).
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[14]	Saravanan. V and Sivakumar. D., A Study on Anti-Fuzzy Subsemiring of a Semiring, International Journal of Computer Applications (0975–8887), Volume 35–No.5, December 2011.
[15]	Saravanan. V and Sivakumar. D, A Study on Anti-Fuzzy Normal Subsemiring of a Semiring, International Mathematical Forum, Vol. 7, 2012, no. 53, 2623–2631.
[16]	Tang J, Zhang X (2001). Product Operations in the Category of L –fuzzy groups. J. Fuzzy Math., 9: 1-10.
[17]	Vasantha Kandasamy. W. B, Smarandache fuzzy algebra, American research press, Rehoboth-2003.
[18]	Zadeh. L. A., Fuzzysets, Information and control, Vol. 8, 338-353 (1965).

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APA Style

Rock Arokiaraj, Vellaiyan Saravanan, Jonadoss Jon Arockiaraj. (2021). A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism. American Journal of Mathematical and Computer Modelling, 6(3), 50-54. https://doi.org/10.11648/j.ajmcm.20210603.12

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ACS Style

Rock Arokiaraj; Vellaiyan Saravanan; Jonadoss Jon Arockiaraj. A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism. Am. J. Math. Comput. Model. 2021, 6(3), 50-54. doi: 10.11648/j.ajmcm.20210603.12

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AMA Style

Rock Arokiaraj, Vellaiyan Saravanan, Jonadoss Jon Arockiaraj. A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism. Am J Math Comput Model. 2021;6(3):50-54. doi: 10.11648/j.ajmcm.20210603.12

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@article{10.11648/j.ajmcm.20210603.12,
  author = {Rock Arokiaraj and Vellaiyan Saravanan and Jonadoss Jon Arockiaraj},
  title = {A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {6},
  number = {3},
  pages = {50-54},
  doi = {10.11648/j.ajmcm.20210603.12},
  url = {https://doi.org/10.11648/j.ajmcm.20210603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20210603.12},
  abstract = {Our motivation in this paper is to start and study the algebraic nature of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. Our purpose of this paper is to initiate and study the notions of (Q,L) - fuzzy normal ℓ-subsemirings of ℓ-semiring.We introduce the concept of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. We study few of their elementary properties by (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring and establish some results on these. These ideas are utilized in the improvement of some significant outcomes. We additionally made an endeavor to study the few properties of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under homomorphism and anti-homomorphism. Also some theorem is the composition operation of functions (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under isomorphism and anti- isomorphism. Also prove some more properties of homomorphism and anti-homomorphism image and pre- image of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring. Finally, we present the theorems of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under image and pre- image of isomorphism and anti- isomorphism.},
 year = {2021}
}

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TY  - JOUR
T1  - A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism
AU  - Rock Arokiaraj
AU  - Vellaiyan Saravanan
AU  - Jonadoss Jon Arockiaraj
Y1  - 2021/09/04
PY  - 2021
N1  - https://doi.org/10.11648/j.ajmcm.20210603.12
DO  - 10.11648/j.ajmcm.20210603.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 50
EP  - 54
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20210603.12
AB  - Our motivation in this paper is to start and study the algebraic nature of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. Our purpose of this paper is to initiate and study the notions of (Q,L) - fuzzy normal ℓ-subsemirings of ℓ-semiring.We introduce the concept of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. We study few of their elementary properties by (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring and establish some results on these. These ideas are utilized in the improvement of some significant outcomes. We additionally made an endeavor to study the few properties of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under homomorphism and anti-homomorphism. Also some theorem is the composition operation of functions (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under isomorphism and anti- isomorphism. Also prove some more properties of homomorphism and anti-homomorphism image and pre- image of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring. Finally, we present the theorems of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under image and pre- image of isomorphism and anti- isomorphism.
VL  - 6
IS  - 3
ER  -

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Author Information

Rock Arokiaraj

Department of Mathematics, Rajiv Gandhi College of Engineering & Technology, Pondicherry, India
Vellaiyan Saravanan

Department of Mathematics, Annamalai University, Annamalainagar, India
Jonadoss Jon Arockiaraj

Department of Mathematics, St. Joseph’s College of Arts & Science, Cuddalore, India

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APA Style

Rock Arokiaraj, Vellaiyan Saravanan, Jonadoss Jon Arockiaraj. (2021). A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism. American Journal of Mathematical and Computer Modelling, 6(3), 50-54. https://doi.org/10.11648/j.ajmcm.20210603.12

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ACS Style

Rock Arokiaraj; Vellaiyan Saravanan; Jonadoss Jon Arockiaraj. A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism. Am. J. Math. Comput. Model. 2021, 6(3), 50-54. doi: 10.11648/j.ajmcm.20210603.12

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AMA Style

Rock Arokiaraj, Vellaiyan Saravanan, Jonadoss Jon Arockiaraj. A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism. Am J Math Comput Model. 2021;6(3):50-54. doi: 10.11648/j.ajmcm.20210603.12

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@article{10.11648/j.ajmcm.20210603.12,
  author = {Rock Arokiaraj and Vellaiyan Saravanan and Jonadoss Jon Arockiaraj},
  title = {A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {6},
  number = {3},
  pages = {50-54},
  doi = {10.11648/j.ajmcm.20210603.12},
  url = {https://doi.org/10.11648/j.ajmcm.20210603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20210603.12},
  abstract = {Our motivation in this paper is to start and study the algebraic nature of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. Our purpose of this paper is to initiate and study the notions of (Q,L) - fuzzy normal ℓ-subsemirings of ℓ-semiring.We introduce the concept of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. We study few of their elementary properties by (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring and establish some results on these. These ideas are utilized in the improvement of some significant outcomes. We additionally made an endeavor to study the few properties of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under homomorphism and anti-homomorphism. Also some theorem is the composition operation of functions (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under isomorphism and anti- isomorphism. Also prove some more properties of homomorphism and anti-homomorphism image and pre- image of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring. Finally, we present the theorems of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under image and pre- image of isomorphism and anti- isomorphism.},
 year = {2021}
}

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TY  - JOUR
T1  - A Study on (Q,L)-fuzzy Normal ℓ-subsemiring of a ℓ-semiring Under Homomorphism and Anti-homomorphism
AU  - Rock Arokiaraj
AU  - Vellaiyan Saravanan
AU  - Jonadoss Jon Arockiaraj
Y1  - 2021/09/04
PY  - 2021
N1  - https://doi.org/10.11648/j.ajmcm.20210603.12
DO  - 10.11648/j.ajmcm.20210603.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 50
EP  - 54
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20210603.12
AB  - Our motivation in this paper is to start and study the algebraic nature of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. Our purpose of this paper is to initiate and study the notions of (Q,L) - fuzzy normal ℓ-subsemirings of ℓ-semiring.We introduce the concept of (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring. We study few of their elementary properties by (Q,L)-fuzzy normal ℓ-subsemirings of a ℓ-semiring and establish some results on these. These ideas are utilized in the improvement of some significant outcomes. We additionally made an endeavor to study the few properties of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under homomorphism and anti-homomorphism. Also some theorem is the composition operation of functions (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under isomorphism and anti- isomorphism. Also prove some more properties of homomorphism and anti-homomorphism image and pre- image of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring. Finally, we present the theorems of (Q,L)-fuzzy normal ℓ-subsemirings of ℓ-semiring under image and pre- image of isomorphism and anti- isomorphism.
VL  - 6
IS  - 3
ER  -

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