On intuitionistic fuzzy quasi ideals of rings with respect to a \(t\)-norm
Downloads
DOI:
https://doi.org/10.26637/MJM0803/0094Abstract
In this paper, the notion of fuzzy quasi ideal is extended to intuitionistic fuzzy quasi ideal with respect to a triangular norm and various results of such intuitionistic fuzzy ideals are studied. It has also been established that if an intuitionistic fuzzy subring with respect to a triangular norm is an intuitionistic fuzzy quasi ideal with respect to that norm, then it is also intuitionistic fuzzy quasi ideal with respect to the annihilation of that triangular norm.
Keywords:
Intuitionistic fuzzy set, Intuitionistic fuzzy subring, Intuitionistic fuzzy quasi ideal, \(t\)-normMathematics Subject Classification:
Mathematics- Pages: 1266-1272
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
Abou-Zaid $S$, On fuzzy ideals and fuzzy quotient rings of a ring. Fuzzy Sets and Systems, 59(1993), 205-210.
Atanassov KT, Intuitionistic fuzzy set. Fuzzy Sets and Systems, 20(1986), 87-96.
Atanassov KT, New operations defined over the Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 61(1994), $137-142$
Banerjee B and Basnet D.Kr, Intuitionistic fuzzy subring and ideals. J.Fuzzy Math., 11(1)(2003), 139-155.
Dheena $mathrm{P}$ and Mohanraaj $mathrm{G}$, T-fuzzy Ideals in Rings, International Journal of Computational Cognition, 9(2)(2011), 98-101.
Dubois D and Prade H, Theory and Applications, Fuzzy Sets and Systems, Academic Press, New York (1978).
Klir GJ, Yuan B, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall of India, Englewood Cliffs (2008).
Kumar R, Fuzzy ideals and fuzzy semi-prime ideals. Some ring theoretic analogues, Information Sci., $46(1992), 43-52$.
Kumar R, Certain fuzzy ideals of rings redefined. Fuzzy Sets and Systems, 46(1992), 251-260.
Liu W, Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets and Systems, 8(1982), 133-139.
Mordeson JN and Malik DS, Fuzzy Commutative Algebra, World Scientific, (1998).
Murugadas $mathrm{P}$ and Vetrivel V, Intuitionistic fuzzy ideals in near rings. Malaya Journal of Matematik, vol.S(1)(2019), 321-326.
Pushkov SG, Fuzzy modules with respect to a t-norm and some of their properties. J Math Sci., 154(30)(2008), $374-378$
Rahman $mathrm{H}$ and Saikia $mathrm{HK}$, Atanassov's intuitionistic fuzzy submodules with respect to a t-norm. Soft Comput., $17(2013), 1253-1262$.
Rasuli R, Norms over intuitionistic fuzzy subrings and ideals of a ring. Notes on Intuitionistic Fuzzy Sets, $22(5)(2016), 72-83$.
Rosenfeld A, Fuzzy groups. J. Math. anal. Appl., $35(1971), 512-517$
Steinfeld, Uher die quasi ideals von halbgruppen. Publ. Math. Debrecen, 4(1956), 262-275.
Zadeh LA, Fuzzy sets. Information and Control, 8(1965), $338-353$.
- NA
Similar Articles
- R.K. Bairwa, Karan Singh, An efficient analytical approach for solving fractional Fokker-Planck equations , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.