Quadri-Polar Fuzzy Fantastic Ideals in BCI-Algebras: A TOPSIS Framework and Application

Authors

  • M. Balamurugan
  • Khalil H. Hakami Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia
  • Moin A. Ansari
  • Anas Al-Masarwah
  • K. Loganathan

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5429

Keywords:

BCK/BCI-algebras, q-polar fuzzy fantastic ideal, q-polar-(ω,ϑ)-fuzzy fantastic ideal, q-polar-(σ~,σ~qτ~)-fuzzy fantastic ideal

Abstract

A quadri-polar fuzzy (qP-F) set is an extension of a traditional fuzzy set that uses four degrees of membership to represent different aspects of belonging to provide a more detailed framework for handling uncertainty and vagueness. In this paper, we propose the notion of quadri-polar-(ϖ,ϑ)-fuzzy fantastic ideals (qP-(ϖ,ϑ)-FFI(s)) in BCI-algebras based on qP-F set. Also, the notion of quadri-polar-(σ~,σ~qτ~)-fuzzy fantastic ideals (qP-(σ~,σ~qτ~)-FFI(s)) is introduced, and the characterizations for an σ~-qP-F set and qτ~-qP-F set to be  quadri-polar fuzzy ideals (qP-FI) in BCI-algebras are established. Furthermore, we present the qP-F TOPSIS technique for multi-criteria Group decision-making (MCGDM), which is a natural extension of the TOPSIS method and used to rank and choose the best alternatives under qP-F positive and negative ideal solutions. Finally, practical examples interpreting the applicability of our proposed qP-F-TOPSIS are solved.

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Quadri-Polar Fuzzy Fantastic Ideals in BCI-Algebras: A TOPSIS Framework and Application. (2024). European Journal of Pure and Applied Mathematics, 17(4), 3129-3155. https://doi.org/10.29020/nybg.ejpam.v17i4.5429