Quadri-Polar Fuzzy Symmetric Ideals in AMR-Algebras: Enhancing Multi-Criteria Decision-Making with a TOPSIS Framework

J.  Eidi; Shuker Khalil; R.  Sabri; R. Vinodkumar; P.  Hemavathi; P.  Muralikrishna

doi:10.5269/bspm.81974

J. Eidi Department of Mathematics, College of Education, Mustensiriyah University, Baghdad, Iraq.
Shuker Khalil University of Basrah http://orcid.org/0000-0002-7635-3553
R. Sabri Department of Mathematics and Computer Applications, College of Applied Sciences, University of Technology, Baghdad, Iraq.
R. Vinodkumar Department of Mathematics,Saveetha Institute of Medical and Technical Sciences, SIMATS, Thandalam-602105, India
P. Hemavathi Department of Mathematics,Rajalakshmi Engineering College(Autonomous), Thandalam-602105, India
P. Muralikrishna PG and Research Department of Mathematics, Muthurangam Government Arts College (Autonomus),Vellore-632002. India

DOI: https://doi.org/10.5269/bspm.81974

Abstract

In recent years, multi-criteria decision-making (MCDM) has gained significant
attention, especially in uncertain and complex environments. Traditional fuzzy set
theory, while effective, often struggles to handle the increased complexity of deci
sion problems involving more than two levels of uncertainty. This paper proposes
the integration of quadri-polar fuzzy sets (q-PF) within the framework of AMR
algebra to address this gap. We introduce a novel approach where the quadri-polar
fuzzy sets, which are capable of handling four distinct levels of uncertainty, are em
ployed to model and evaluate complex decision-making problems more accurately.
To solve such problems, we propose a TOPSIS (Technique for Order of Preference by
Similarity to Ideal Solution) framework, adapted to the quadri-polar fuzzy setting.
This enhanced TOPSIS model incorporates the unique characteristics of q-PF sets,
thus providing a more robust and reliable decision-making tool. We also present a
real-world application to demonstrate the efficacy of this approach in solving prac
tical MCDM problems. The results suggest that the proposed model outperforms
traditional fuzzy-based approaches, particularly in scenarios where uncertainty is
represented by multiple levels of fuzzy information

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