Direct product of finite anti fuzzy normal sub-rings over non-associative rings

Volume 22, Issue 4, pp 399--411 http://dx.doi.org/10.22436/jmcs.022.04.08

Publication Date: September 21, 2020 Submission Date: July 12, 2020 Revision Date: August 08, 2020 Accteptance Date: August 17, 2020

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Authors

Nasreen Kausar - Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan. Mohammad Munir - Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan. Salahuddin - Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia. Zuhairi Baharudin - Department of Electrical and Electronics Engineering, University of Teknologi Petronas, Seri Iskandar, Malaysia. Badar Ul Islam - Department of Electrical Engineering, NFC IEFR FSD, Pakistan.

Abstract

In this paper, we define the concept of direct product of finite anti fuzzy normal sub-rings over non-associative and noncommutative rings LA-rings and investigate the some fundamental properties of direct product of anti fuzzy normal sub-rings.

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Keywords

• Direct product of fuzzy sets
• anti fuzzy LA-sub-rings
• anti fuzzy normal LA-sub-rings

MSC

•  03F55
•  08A72
•  20N25

References

• [1] M. T. Abu Osman, On the direct product of fuzzy subgroups, Fuzzy Sets and Systems, 12 (1984), 87--91
  • View Article
  • MathSciNet


• [2] M. T. Abu Osman, On some product of fuzzy subgroups, Fuzzy Sets and Systems, 24 (1987), 79--86
  • View Article


• [3] S. Abou-Zaid, On normal fuzzy subgroups, J. Fac. Educ. Ain Shams Univ. Cairo., 13 (1988), 115--125
  • Google Scholar


• [4] M. Akram, K. H. Dar, On anti fuzzy left h-ideals in hemirings, Int. Math. Forum, 2 (2007), 2295--2304
  • View Article
  • MathSciNet


• [5] E. F. Alharfie, N. Muthana, The commutativity of prime rings with homoderivations, Int. J. Adv. Appl. Sci., 5 (2018), 79--81
  • View Article


• [6] R. Biswas, Fuzzy subgroups and anti fuzzy subgroups, Fuzzy Sets and Systems, 35 (1990), 121--124
  • View Article
  • MathSciNet


• [7] J. R. Cho, J. Jezek, T. Kepka, Paramedial groupoids, Czechoslovak Math. J., 49 (1999), 277--290
  • View Article


• [8] K. A. Dib, N. Galhum, A. A. M. Hassan, Fuzzy rings and fuzzy ideals, Fuzzy Math., 4 (1996), 245--261
  • MathSciNet
  • Google Scholar


• [9] V. N. Dixit, R. Kumar, N. Ajmal, Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets and Systems, 44 (1991), 127--138
  • View Article
  • MathSciNet


• [10] K. C. Gupta, M. K. Kantroo, The intrinsic product of fuzzy subsets of a ring, Fuzzy Sets and Systems, 57 (1993), 103--110
  • View Article
  • MathSciNet


• [11] S. M. Hong, Y. B. Jun, Anti fuzzy ideals in BCK-algebra, Kyungpook Math. J., 38 (1998), 145--150
  • View Article
  • MathSciNet


• [12] J. Ježek, T. Kepka, Medial groupoids, Rozpravy CSAV Rada Mat. a Prir. Ved., 93 (1993), 93 pages
  • MathSciNet
  • Google Scholar


• [13] T. Kadir, In discrepancy between the traditional Fuzzy logic and inductive, Int. J. Adv. Appl. Sci., 1 (2014), 36--43
  • View Article


• [14] M. S. Kamran, Conditions for LA-semigroups to resemble associative structures, Ph.D. Thesis, Quaid-i-Azam University, Islamabad (1993)
  • Google Scholar


• [15] N. Kausar, Direct product of finite intuitionistic anti fuzzy normal sub-rings over non-associative rings, Eur. J. Pure Appl. Math., 12 (2019), 622--648
  • View Article


• [16] N. Kausar, M. Alesemi, S. Salahuddin, M. Munir, A study on Ordered AG-groupoid by their fuzzy interior ideals, Int. J. Adv. Appl. Sci., 7 (2020), 75--82
  • View Article


• [17] N. Kausar, B. ul Islam, S. A. Ahmad, M. A. Waqar, Intuitionistics fuzzy ideals with thresholds (α, β] in LA-rings, Eur. J. Pure Appl. Math., 12 (2019), 906--943
  • View Article
  • Google Scholar


• [18] N. Kausar, B. U. Islam, M. Y. Javaid, S. A. Ahmad, U. Ijaz, Characterizations of non-associative rings by the properties of their fuzzy ideals, J. Taibah. Univ. Sci., 13 (2019), 820--833
  • View Article
  • Google Scholar


• [19] N. Kausar, M. A. Waqar, Characterizations of non-associative rings by their intuitionistic fuzzy bi-ideals, Eur. J. Pure Appl. Math., 12 (2019), 226--250
  • View Article
  • MathSciNet


• [20] N. Kausar, M. A. Waqar, Product of finite fuzzy normal sub-rings over non-associative rings, Int. J. Anal. Appl., 17 (2019), 752--770
  • View Article


• [21] M. A. Kazim, M. Naseeruddin, On almost semigroups, Aligarh Bull. Math., 2 (1972), 1--7
  • MathSciNet
  • Google Scholar


• [22] N. Kuroki, Regular fuzzy duo rings, Inf. Sci., 94 (1996), 119--139
  • View Article
  • MathSciNet


• [23] A. Lafi, DFIG control: A fuzzy approach, Int. J. Adv. Appl. Sci., 6 (2019), 107--116
  • View Article


• [24] W. J. Liu, Fuzzy invariant subgroups and ideals, Fuzzy Sets and Systems, 8 (1982), 133--139
  • View Article
  • MathSciNet


• [25] T. K. Mukherjee, M. K. Sen, On fuzzy ideals of a ring I, Fuzzy Sets and Systems, 21 (1987), 99--104
  • View Article
  • MathSciNet
  • Google Scholar


• [26] T. K. Mukherjee, M. K. Sen, Prime fuzzy ideals in rings, Fuzzy Sets and Systems, 32 (1989), 337--341
  • View Article
  • MathSciNet


• [27] M. Munir, N. Kausar, Salahuddin, Tehreem, On the prime fuzzy m-bi ideals in semigroups, J. Math. Computer Sci., 21 (2020), 357--365
  • View Article


• [28] P. V. Protić, N. Stevanović,, AG-test and some general properties of Abel-Grassmann’s groupoids, Pure Math. Appl., 6 (1995), 371--383
  • View Article
  • MathSciNet


• [29] A. K. Ray, On product of fuzzy subgroups, Fuzzy Sets and Systems, 105 (1999), 181--183
  • View Article
  • MathSciNet


• [30] T. Shah, N. Kausar, I. Rehman, Intuitionistic fuzzy normal sub-rings over a non-associative ring, An. Stiint. Univ. ”Ovidius” Constanta Ser. Mat., 20 (2012), 369--386
  • View Article
  • Google Scholar


• [31] T. Shah, I. Rehman, On LA-rings of finitely non-zero functions, Int. J. Contemp. Math. Sci., 5 (2010), 209--222
  • View Article
  • Google Scholar


• [32] H. Sherwood, On product of fuzzy subgroups, Fuzzy Sets and Systems, 11 (1983), 79--89
  • View Article


• [33] U. M. Swamy, K. L. N. Swamy, Fuzzy prime ideals of rings, J. Math. Anal. Appl., 134 (1988), 94--103
  • View Article
  • MathSciNet


• [34] L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338--353
  • View Article
  • MathSciNet
  • Google Scholar