New Type of Fuzzy Algebra Structure Setting Complex Bipolar Neutrosophic Sets of Bisemirings

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DOI: https://doi.org/10.28924/2291-8639-23-2025-25
Published: Jan 27, 2025
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M. Palanikumar, T.T. Raman, Aiyared Iampan, New Type of Fuzzy Algebra Structure Setting Complex Bipolar Neutrosophic Sets of Bisemirings, Int. J. Anal. Appl., 23 (2025), 25.

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M. Palanikumar, T.T. Raman, Aiyared Iampan

Abstract

The notion of complex bipolar neutrosophic subbisemirings (CBNSBSs) is constructed and analyzed. We examine the significant characteristics and homomorphic features of CBNSBSs. We propose the CBNSBS level sets for bisemirings. Suppose that \(\Bbbk\) is a subset of \(\mathfrak{S}\). Then \(R = \left( {\complement_{\Bbbk}^{{T^{-}}}} \cdot e^{i\omega {\Finv_{\Bbbk}^{{T^{-}}}}},\ {\complement_{\Bbbk}^{{I^{-}}}} \cdot e^{i\omega {\Finv_{\Bbbk}^{{I^{-}}}}},\ {\complement_{\Bbbk}^{{F^{-}}}} \cdot e^{i\omega {\Finv_{\Bbbk}^{{F^{-}}}}},\ {\complement_{\Bbbk}^{{T^{+}}}} \cdot e^{i\omega {\Finv_{\Bbbk}^{{T^{+}}}}},\ {\complement_{\Bbbk}^{{I^{+}}}} \cdot e^{i\omega {\Finv_{\Bbbk}^{{I^{+}}}}},\ {\complement_{\Bbbk}^{{F^{+}}}} \cdot e^{i\omega {\Finv_{\Bbbk}^{{F^{+}}}}}\right)\) is a CBNSBS of \(\mathfrak{S}\) if and only if \({\complement^{(\hslash_{1},\hslash_{2})}}\) is a subbisemiring (SBS) of \(\mathfrak{S}\) for all \((\hslash_{1},\hslash_{2}) \in [-1,0] \times [0,1]\). It is demonstrated that all CBNSBSs have homomorphic images, and all CBNSBSs have homomorphic pre-images. Examples are provided to show how our findings are used.

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References

  1. J. Ahsan, K. Saifullah, M.F. Khan, Fuzzy Semirings, Fuzzy Sets Syst. 60 (1993), 309–320. https://doi.org/10.1016/0165-0114(93)90441-J.
  2. S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical Fuzzy Sets and Their Applications in MultiAttribute Decision Making Problems, J. Intell. Fuzzy Syst. 36 (2019), 2829–2844. https://doi.org/10.3233/JIFS-172009.
  3. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3.
  4. B.C. Cuong, V. Kreinovich, Picture Fuzzy Sets - A New Concept for Computational Intelligence Problems, in: 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, Hanoi, Vietnam, 2013: pp. 1–6. https://doi.org/10.1109/WICT.2013.7113099.
  5. J.S. Golan, Semirings and Their Applications, Springer Netherlands, Dordrecht, 1999. https://doi.org/10.1007/978-94-015-9333-5.
  6. F. Hussian, R.M. Hashism, A. Khan, M. Naeem, Generalization of Bisemirings, Int. J. Comput. Sci. Inf. Secur. 14 (2016), 275-289.
  7. K.M. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, in: Proceedings of International Conference on Intelligent Technologies, Bangkok, Thailand, (2000), 307-312.
  8. M. Palanikumar, K. Arulmozhi, MCGDM Based on TOPSIS and VIKOR Using Pythagorean Neutrosophic Soft With Aggregation Operators, Neutrosophic Sets Syst. 51 (2022), 538-555.
  9. M. Palanikumar, K. Arulmozhi, Novel Possibility Pythagorean Interval Valued Fuzzy Soft Set Method for a Decision Making, TWMS J. Appl. Eng. Math. 13 (2023), 327-340.
  10. M. Palanikumar, K. Arulmozhi, On Intuitionistic Fuzzy Normal Subbisemirings of Bisemirings, Nonlinear Stud. 28 (2021), 717-721.
  11. M. Palanikumar, K. Arulmozhi, A. Iampan, Multi Criteria Group Decision Making Based on VIKOR and TOPSIS Methods for Fermatean Fuzzy Soft With Aggregation Operators, ICIC Express Lett. 16 (2022), 1129-1138. https://doi.org/10.24507/icicel.16.10.1129.
  12. M. Palanikumar, S. Broumi, Square Root Diophantine Neutrosophic Normal Interval-Valued Sets and Their Aggregated Operators in Application to Multiple Attribute Decision Making, Int. J. Neutrosophic Sci. 19 (2022), 63-84. https://doi.org/10.54216/IJNS.190307.
  13. M. Palanikumar, N. Kausar, H. Garg, A. Iampan, S. Kadry, M. Sharaf, Medical Robotic Engineering Selection Based on Square Root Neutrosophic Normal Interval-Valued Sets and Their Aggregated Operators, AIMS Math. 8 (2023), 17402–17432. https://doi.org/10.3934/math.2023889.
  14. M. Palanikumar, G. Selvi, G. Selvachandran, S.L. Tan, New Approach to Bisemiring Theory via the Bipolar-Valued Neutrosophic Normal Sets, Neutrosophic Sets Syst. 55 (2023), 427-450.
  15. S.G. Quek, H. Garg, G. Selvachandran, M. Palanikumar, K. Arulmozhi, VIKOR and TOPSIS Framework With a Truthful-Distance Measure for the (t,s)-Regulated Interval-Valued Neutrosophic Soft Set, Soft Comput. 28 (2024), 553. https://doi.org/10.1007/s00500-023-08338-y.
  16. D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex Fuzzy Sets, IEEE Trans. Fuzzy Syst. 10 (2002), 171–186. https://doi.org/10.1109/91.995119.
  17. M.K. Sen, S. Ghosh, S. Ghosh, An Introduction to Bisemirings, Southeast Asian Bull. Math. 28 (2004), 547-559.
  18. F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, in: Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, 2003.
  19. R.R. Yager, Pythagorean Membership Grades in Multicriteria Decision Making, IEEE Trans. Fuzzy Syst. 22 (2014), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989.
  20. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.