Home 9 Volume 9 Fuzzy soft tri-ideals over Gamma-semirings
Open AccessArticle
Fuzzy soft tri-ideals over Gamma-semirings

Department of Mathematics, Sankethika Institute of Tech. And Management, Visakhapatnam 530 041, A.P. India.

Department of Mathematics, GSS, Gitam (Deemed To Be University), Visakhapatnam 530 045, A.P. India.

Department of Mathematics, Bapatla Engineering College, Bapatla 522 101, A.P. India.

* Corresponding Author
Annals of Communications in Mathematics 2023
, 6 (4),
225-237.
https://doi.org/10.62072/acm.2023.060403
Received: 21 September 2023 |
Accepted: 21 November 2023 |
Published: 31 December 2023

Abstract

In this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.

Keywords

Cite This Article

M. Murali Krishna Rao, Noorbhasha Rafi, Rajendra Kumar Kona*.
Fuzzy soft tri-ideals over Gamma-semirings.

Annals of Communications in Mathematics,

2023,
6 (4):
225-237.
https://doi.org/10.62072/acm.2023.060403
References

[1] U. Acar, F. Koyuncu and B. Tanay. Soft sets and Soft rings, Comput. and Math. with Appli., 59(2010), 3458–346.
[2] H. Aktas and N. Cagman. Soft sets and soft groups. Infor. Sci., 177(2007), 2726–2735.
[3] A. Borumand Saeid, M. Murali Krishna Rao, K. Rajendra Kumar and N. Rafi. Fuzzy (Soft) Quasi-Interior Ideals of Semirings, Trans. Fuzzy Sets Syst.,1(2) (2022), 129–141.
[4] F. Feng, Y.B. Jun and X. Zhao. Soft semirings, Comput. and Math. with Appli., 56(2008), 2621–2628.
[5] J.Ghosh, B.Dinda and T.K. Samanta. Fuzzy soft rings and Fuzzy soft ideals, Int. J. P. App. Sc. Tech., 2(2)(2011), 66–74.
[6] R. A. Good and D. R. Hughes. Associated groups for a semigroup, Bull. Amer. Math. Soc., 58(1952), 624–625.
[7] N. Kuroki. On fuzzy semigroups, Information Sciences, 53(3) (1991), 203–236.
[8] P. K. Maji, R. Biswas and A. R. Roy. Fuzzy soft sets, J. Fuzzy Math., 9(3) (2001), 589–602.
[9] D. Molodtsov. Soft set theory-First results, Comput. Math. Appl., 37(1999), 19–31.
[10] M. Murali Krishna Rao. Γ− semirings-I, Southeast Asian Bull. Math., 19(1) (1995), 49–54.
[11] M. Murali Krishna Rao. Tri-quasi ideals of Γ−semirings, Disc. Math. General Algebra and Appli., 41 (2021), 33–44.
[12] M. Murali Krishna Rao. Fuzzy soft bi-interior ideals over Γ−semirings, Journal of Hyperstructures, 10(1) (2021), 47–62.
[13] M. Murali Krishna Rao. Tri-ideals and Fuzzy tri-ideals of Γ−semirings, Annals. of Fuzzy Math. and Inform., 18 (2) (2019), 181–193.
[14] M. Murali Krishna Rao, K. Rajendra Kumar and Arsham Borumand Saeid. Hesitant Fuzzy Ideals of (Ordered) Γ Semirings, New Mathematics and Natural Computation (2024), 1–19
[15] M. Murali Krishna Rao. Quasi-interior ideals and weak-interior ideals, Asia Pac. J. Math., (2020), 7–21.
[16] M. Murali Krishna Rao. A study of ideals of Γ-Semiring with involution , Bull. of Int. Math. Virtual Institute. 13 (1) (2023), 83–93.
[17] M. K. Sen. On Γ−semigroup, Proc. of International Conference of algebra and its application, (1981), Decker Publicaiton, New York, 301–308.
[18] L. A. Zadeh. Fuzzy sets, Information and control, 8 (1965), 338–353.

  • Creative Commons License
  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

    0 Comments

    Submit a Comment

    Your email address will not be published. Required fields are marked *

    Preview PDF

    XML File

    Loading

    Share