A robust SR-complex fuzzy MCDM framework with lie algebraic foundations for AI-assisted tuberculosis diagnosis

Manivannan Balamurugan; Ganesan Ellammal; Zaid Bassfar; Abdulaziz Mohammed Alanazi; Kandhasamy Tamilvanan; Manivannan Balamurugan; Ganesan Ellammal; Zaid Bassfar; Abdulaziz Mohammed Alanazi; Kandhasamy Tamilvanan

doi:10.3934/math.2026664

AIMS Mathematics

2026, Volume 11, Issue 6: 16144-16173. doi: 10.3934/math.2026664

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Research article

A robust SR-complex fuzzy MCDM framework with lie algebraic foundations for AI-assisted tuberculosis diagnosis

1.
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India
2.
Faculty of Computing and Information Technology, University of Tabuk, PO. Box 741, Tabuk 71491, Saudi Arabia
3.
Department of Mathematics, University of Tabuk, PO. Box 741, Tabuk 71491, Saudi Arabia
4.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India

Received: 09 April 2026 Revised: 22 May 2026 Accepted: 27 May 2026 Published: 08 June 2026
MSC : 03E72, 08A72, 22E60, 62F07, 90C70

In this study, a square-root-complex fuzzy set (SR-CFS) frame is introduced to associate Lie algebraic structures for modeling interaction-aware hesitancy in multi-criteria decision making processes. Instead of using real-valued memberships as in classical fuzzy extensions, our method deals with squared and square-rooted complex membership values and phase elements simultaneously to show the strength of evidence, uncertainty, and disagreement among experts. In this structure, we define SR-complex fuzzy Lie subalgebras (SR-CFLSAs) and SR-complex fuzzy Lie ideals (SR-CFLIDs) and illustrate their basic properties. They consist of stability under Lie algebra homomorphisms, which ensure that the structure of uncertainty is preserved during algebraic operations. Based on these theories, we combine SR-CFS with the PROMETHEE Ⅱ and VIKOR methods to develop an integrated decision-making system to deal with interdependent criteria effectively. The work includes an extensive case study on AI-assisted diagnosis of newborn tuberculosis, where we derive decision matrices from expert evaluations and clinical performance metrics.
- Lie algebra,
- SR-complex fuzzy set,
- SR-complex fuzzy subalgebra,
- SR-complex fuzzy Lie ideal,
- PROMETHEE Ⅱ,
- VIKOR
Citation: Manivannan Balamurugan, Ganesan Ellammal, Zaid Bassfar, Abdulaziz Mohammed Alanazi, Kandhasamy Tamilvanan. A robust SR-complex fuzzy MCDM framework with lie algebraic foundations for AI-assisted tuberculosis diagnosis[J]. AIMS Mathematics, 2026, 11(6): 16144-16173. doi: 10.3934/math.2026664

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Abstract

In this study, a square-root-complex fuzzy set (SR-CFS) frame is introduced to associate Lie algebraic structures for modeling interaction-aware hesitancy in multi-criteria decision making processes. Instead of using real-valued memberships as in classical fuzzy extensions, our method deals with squared and square-rooted complex membership values and phase elements simultaneously to show the strength of evidence, uncertainty, and disagreement among experts. In this structure, we define SR-complex fuzzy Lie subalgebras (SR-CFLSAs) and SR-complex fuzzy Lie ideals (SR-CFLIDs) and illustrate their basic properties. They consist of stability under Lie algebra homomorphisms, which ensure that the structure of uncertainty is preserved during algebraic operations. Based on these theories, we combine SR-CFS with the PROMETHEE Ⅱ and VIKOR methods to develop an integrated decision-making system to deal with interdependent criteria effectively. The work includes an extensive case study on AI-assisted diagnosis of newborn tuberculosis, where we derive decision matrices from expert evaluations and clinical performance metrics.

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