A Study on Some Relations on Multi-Fuzzy (Left-Right) Ideals of Rings
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Multi-Fuzzy Set, Multi Fuzzy Ring, Multi Fuzzy Left (Right) Ideals, Homomorphism of Multi-Fuzzy Ideal of A Ring, Cartesian Product of Multi-Fuzzy Sets
Abstract
Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi-dimensional fuzziness. In this paper, we introduce the concepts of multi-fuzzy rings, multi-fuzzy ideals, the image of a multi-fuzzy ideal of a ring under a homomorphism, the Cartesian product of multi-fuzzy sets, and some related properties and theorems. The purpose of this study is to implement the fuzzy set theory and rings theory in multi-fuzzy rings.
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References
[1]- L.A. Zadeh., (1965) Fuzzy Sets, Information and Control, 8,338-353.
[2]- Rosenfeld, A, (1971)Fuzzy groups, Journal of Mathematical Analysis and applications, 35 , 512 – 517.
[3]- Biswas.R., (1990) fuzzy subgroups and Anti-fuzzy subgoups, Fuzzy sets and Systems, 5, 121 – 124.
[4]- W. J. Liu, (1982) “Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, vol. 8, no. 2, pp. 133–139.
[5]- Z . Yue. (1988) Prime L-fuzzy ideal and primary, FSS, 27 345-350.
[6]- T.K.Mukharjee and S.K.Sen: (1989)Prime fuzzy ideals in ring. FSS, 32337-341.
[7]- U.U. Swami, D. V. Raju : (1991) Irreducibility in algebraic fuzzy systems : Fuzzy sets and systems, 41,233-241.
[8]- V.N. Dixit, R. Kumar, N. Ajma: (1992) On fuzzy rings, FSS, 49 205-213.
[9]- R. Kumar: (1992) certain fuzzy ideals of rings redephined, FSS, 46 (251-260.
[10]- X. Y. Zie.(2008) On prime fuzzy ideals of a semigroup : J.fuzzy Math, (4),231-241.
[11]- Azam.F.A, A.A.Mamun, and F. Nasrin, (2013)Anti fuzzy ideals of a ring, Annals of Fuzzy Mathematics and Informatics, Volume 5, No.2, pp 349 – 360.
[12]- S. Abou-Zaid, (1991) “On fuzzy subnear-rings and ideals” Fuzzy Sets and Systems, vol. 44, no. 1, pp. 139–146.
[13]- Sabu Sebastian and T.V. Ramakrishnan., (2010)Multi-Fuzzy Sets, International Mathematical Forum, 5, no. 50, 2471-2476, Al-Tahan, M.; Hoskova.
[14]- T.V. Ramakrishnan and Sabu Sebastian., (2010) A Study on Multi-fuzzy Sets, International Journal of Applied Mathematics, Vol. 23, No.4, 713-721.
[15]- Muthuraj. R and Balamurugan. S,(2013)Multi-fuzzy group and its level subgroups, Gen.Math.Notes, Vol. 17, No. 1, pp 74 – 81.
[16]- Muthuraj. R and Malarselvi. C, (2014) Multi-anti Fuzzy Ideal of a Ring, Proceedings of the National Converence on Mathematical Modellig, 114 – 120.
[17]- Shinoj, T.K.; Baby, A.; John, S.J.,( 2015) On some algebraic structures of fuzzy multisets. Ann. Fuzzy Math. Inform. 9, 77–90.
[18]- Al-Tahan, M.; Hoskova-Mayerova, S.; Davvaz, B.( 2020) Fuzzy multi-polygroups. J. Intell. Fuzzy Syst, 38, 2337–2345.
[19]- Miyamoto, S. (2000) Fuzzy Multisets and Their Generaliza- tions, Multiset Processing; Lecture Notes in Computer Science 2235, Germany, pp. 225–236.
[20]- Hoskova-Mayerova., S.; Al Tahan, M. (2021) Anti-Fuzzy Multi-Ideals of Near Ring. Mathematics, 9, 494.
[21]- Mayerova, S.; Davvaz, B., (2019) Some results on (generalized) fuzzy multi-Hv-ideals of Hv-rings. Symmetry, 11, 1376.
[22]- R.Muthuraj, C. Malarselvi., (2015) Homomorphism and Anti-homomorphism of Multi-Fuzzy Ideal and Multi-Anti Fuzzy Ideal of a Ring. IOSR Journal of Mathematics, PP 83-94e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11.
[23]- Muthuraj. R and Malarselvi. C., (2014) Multi-Fuzzy Prime Ideal of a Ring, Discovery, Volume 21, No. 65.
[24]- Lokavarapu Sujatha., (2014)Multi fuzzy subrings and ideals. Annals of Fuzzy Mathematics and Informatics Volume x, No. x, (mm 201y)m.
[25]- R.Muthuraj, C. Malarselvi., (2017) Cartesian product of multi-fuzzy ideal of a ring, International Journal of Computational and Applied Mathematics. ISSN 1819-4966 Volume 12, Number 1.
[26]- Gezahagne Addis, Nasreen Kausar, Mohammad Munir. (2020) Fuzzy homomorphism theorems on rings. Journal of Discrete Mathematics Sciences and Cryptography.ISSN: 0972-0529(print) ISSN 2169-0065(Online).
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