Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON BIPOLAR M - N-MULTI Q-FUZZY SUBGROUPS

  • MOURAD OQLA MASSA'DEH (Department of Applied science, Ajloun collage, Al-Balqa Applied university) ;
  • AHLAM FALLATAH (Department of Mathematics, College of Sciences, Taibah University)
  • Received : 2020.09.18
  • Accepted : 2023.05.04
  • Published : 2023.07.30
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Abstract

For any bipolar multi Q-fuzzy set δ of an universe set G, we redefined a normal, conjugate concepts, union and product operations of a bipolar M - N-multi Q-fuzzy subgroups and we discuss some of its properties. On the other hand, we introduce and define the level subsets positive β-cut and negative α-cut of bipolar M - N- multi Q- fuzzy subgroup and discuss some of its related properties.

Keywords

Acknowledgement

The authors are thankful to the referees for their valuable comments and suggestions for improving the article.

References

  1. L.A. Zadeh, Fuzzy sets, Information and control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  2. A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  3. W.M. Wu, Normal Fuzzy Subgroups, Fuzzy Math. 1 (1981), 21-23.
  4. R. Biswas, Fuzzy groups and Anti-fuzzy subgroup, Fuzzy sets and Systems 35 (1990), 121-124. https://doi.org/10.1016/0165-0114(90)90025-2
  5. M.O. Mourad, P and P * upper fuzzy subgroups, Far East journal of Mathematics Sciences 5 (2010), 97-104.
  6. W.R. Zhang, L. Zhang and Yin Yang, Bipolar Logic and Bipolar Fuzzy Logic, Inform Sci. 165 (2004), 265-287. https://doi.org/10.1016/j.ins.2003.05.010
  7. M.S. Anithar, K.L. Murugan antha Prasad and K. Arjunan, Note on Bipolar Valued Fuzzy Subgroups of a Group, Bulleten of Society for Mathematical Services and Standards 2 (2013), 52-59.
  8. M.O. Mourad, On Bipolar Fuzzy Cosets, Bipolar Fuzzy Ideals and Isomorphism of Γ-Near Rings, Far East Journal of Mathematical Sciences 102 (2017), 731-747.
  9. T.A. Ali and R. Hossein, Complement and Isomorphism on Bipolar Fuzzy Graphs, Fuzzy Inf. Eng. 6 (2014), 505-522. https://doi.org/10.1016/j.fiae.2015.01.007
  10. Z.A. Wael, A.M. Asa'd, H.M. Hazem, W. Youssef and M.O. Mourad, Introduction to Cartesian, Tensor and Lexicographic Product of Bipolar Interval Valued Fuzzy Graph, Journal of Engineering and Applied Sciences 15 (2020), 581-585.
  11. S.S. Arockiaselvi, S. Naganathan and K. Arjunan, Properties of Bipolar-Valued Q-Fuzzy Subgroups of a Group, International Journal of Mathematical Archive 7 (2016), 117-121.
  12. M.O. Mourad and F.A. Ali, Bipolar Valued Q-Fuzzy HX Subgroup on an HX Group, Journal of Applied Computer Science and Mathematics 11 (2017), 20-24. https://doi.org/10.4316/JACSM.201701004
  13. M.O. Mourad, A Study on Anti Bipolar Q-Fuzzy Normal Semi Groups, Journal of Mathematical Sciences and Applications 6 (2018), 1-5. https://doi.org/10.12691/jmsa-6-1-1
  14. M.O. Mourad and I. Farhan, Bipolar Q-Fuzzy H-Ideals over Γ-Hemiring, Advances in Fuzzy Mathematics 13 (2018), 15-24.
  15. A. Solairaju and A. Prasanna, New Structure of Fuzzy Fully Invariant Bipolar Q-Fuzzy Regular Lattices, International Journal of Computer Applications 8 (2011), 22-25. https://doi.org/10.5120/2264-2913
  16. M.O. Mourad, The M - N-Homomorphism and M - N-Anti Homomorphism over M - N-Fuzzy Subgroups, Int. J. of Pure and Appl. Math. 78 (2012), 1019-1027.
  17. M. Kaliraja and S. Rumenaka, M - N-Fuzzy Normal Soft Groups, Intern. J. Fuzzy Mathematical Archive 13 (2017), 159-165. https://doi.org/10.22457/ijfma.v13n2a6
  18. M. Kaliraja and S. Rumenaka, M - N-Anti Fuzzy Normal Soft Groups, Int. J. Math. And Appl. 6 (2018), 1035-1042.
  19. S. Sabu and T.V. Ramakrishnan, Multi-Fuzzy Sets, International Mathematical Forum 50 (2010), 2471-2476.
  20. Muthuraj and S. Balamurugan, A Study on Intuitionistic Multi-Anti Fuzzy Subgroups, International Journal of Application of Fuzzy Sets and Artificial intelligence 4 (2014), 153-172.
  21. R. Muthuraj and S. Devi, Multi-Fuzzy Subalgebras of BG-Algebra and Its Level Subalgebras, International Journal of Applied Mathematical Sciences 9 (2016), 113-120.