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

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), 2021. 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

References
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[3] Asok Kumer Ray, On product of fuzzy subgroups, fuzzy sets and sysrems, 105, 181-183 (1999).
[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).
[6] Mustafa Akgul, Some properties of fuzzy groups, Journal of mathematical analysis and applications, 133, 93-100 (1988).
[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).
[13] Sivaramakrishnadas. P, Fuzzy groups and level subgroups, Journal of Mathematical Analysis and Applications, 84, 264-269 (1981).
[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.
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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
  • Department of Mathematics, Rajiv Gandhi College of Engineering & Technology, Pondicherry, India

  • Department of Mathematics, Annamalai University, Annamalainagar, India

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

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