The projection and utilization of Neutrosophic algebra for decision-making processes

Authors

  • Joseph Oluwakorede Campbell Department of Mathematics, University of Lagos, Akoka, Nigeria.
  • Adebisi Sunday Adesina * Department of Mathematics, University of Lagos, Akoka, Nigeria.

https://doi.org/10.48314/caa.vi.39

Abstract

Neutrosophic algebra is an emerging field that extends classical algebra by incorporating the concept of neutrosophy, which deals with the study of indeterminacy. This work projects the theoretical foundations of Neutrosophic algebra and its applications to decision-making in areas of importance. By leveraging several Neutrosophic principles, which introduces the notion of truth, falsehood, and indeterminacy simultaneously, Neutrosophic algebra offers a robust framework for addressing problems in various domains where uncertainty, ambiguity, and incomplete information prevail.

Keywords:

Neutrosophic algebra, Decision-making processes, Indeterminacy, Fuzzy set and logic, Uncertainties, Inconsistencies

References

  1. [1] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
  2. [2] Salii, V. (1965). Binary L-relations. Izvestiya vysshikh uchebnykh zavedenii. matematika, 44(1), 133–145. (In Russian). https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=2487.
  3. [3] Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics, 24(3), 287. https://fs.unm.edu/IFS-generalized.pdf
  4. [4] Smarandache, F. (1999). A unifying field in logics: Neutrosophic logic. American Research Press, 1-141. https://web-archive.southampton.ac.uk/cogprints.org/1919/3/eBook-Neutrosophics2.pdf
  5. [5] Smarandache, F. (2003). Neutrosophic probability, set, and logic: Analytic synthesis & synthetic analysis. American Research Press. https://fs.unm.edu/Neutrosophic3.pdf
  6. [6] Kandasamy, W. B. V., & Smarandache, F. (2006). Neutrosophic rings. Infinite Study. https://arxiv.org/pdf/math/0607765
  7. [7] Smarandache, F. (2005). Introduction to neutrosophic algebra. American Research Press. https://fs.unm.edu/IntroductionNeutrosophicAlgebra.pdf
  8. [8] Chen, S. M. (2011). Neutrosophic sets and their applications. Journal of intelligent & fuzzy systems, 21(1), 15–26. https://doi.org/10.3233/IFS-2007-00352
  9. [9] Smarandache, F., & Dezert, J. (2014). Advances and applications in neutrosophic logic and Neutrosophic set theory. Phoenix: Infinite Study Press. https://fs.unm.edu/NeutrosophicBook1.pdf
  10. [10] Zhang, Z., & Wu, C. (2014). A novel method for single-valued Neutrosophic multi-criteria decision making with incomplete weight information. Neutrosophic sets and systems, 4(1), 35–49. https://digitalrepository.unm.edu/nss_journal/vol4/iss1/6/
  11. [11] Abdel‑Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. (2018). A hybrid approach of neutrosophic sets and DEMATEL method for developing supplier selection criteria. Design automation for embedded systems, 22(4), 257–278. https://doi.org/10.1007/s10617-018-9203-6
  12. [12] Abdel‑Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. (2019). A group decision making framework based on neutrosophic TOPSIS approach for smart medical device selection. Journal of medical systems, 43(3). https://doi.org/10.1007/s10916-019-1156-1
  13. [13] Smarandache, F., & Pramanik, S. (2016). New trends in Neutrosophic theory and applications. ArXiv preprint. https://doi.org/10.48550/arXiv.1611.08555

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Published

2025-03-03

Issue

Vol. 2 No. 1 (2025): Complexity Analysis and Applications

Section

Articles

Categories

How to Cite

The projection and utilization of Neutrosophic algebra for decision-making processes. (2025). Complexity Analysis and Applications, 2(1), 12-24. https://doi.org/10.48314/caa.vi.39