TODIM method with unknown weights under t-arbicular fuzzy environment for optimal gate security system selection

Jawad Ali; Ioan-Lucian Popa; Jawad Ali; Ioan-Lucian Popa

doi:10.3934/math.2025627

AIMS Mathematics

2025, Volume 10, Issue 6: 13941-13973. doi: 10.3934/math.2025627

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TODIM method with unknown weights under t-arbicular fuzzy environment for optimal gate security system selection

Jawad Ali ¹,
Ioan-Lucian Popa ^{2,3
,
,}

1.
Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KPK, Pakistan
2.
Department of Computing, Mathematics and Electronics, "1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania
3.
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania

Received: 08 March 2025 Revised: 05 April 2025 Accepted: 09 April 2025 Published: 17 June 2025
MSC : 03E72, 90B50, 68T35

This study introduces the t-arbicular fuzzy (t-AF) set, an extension of the t-spherical fuzzy set, to enhance decision-making in complex environments. The research focuses on the theoretical foundation of the t-AF set, encompassing the development of algebraic operations and comparison rules. In addition, we propose novel aggregation operators (AOs), including the t-AF weighted average (t-AFWA) and t-AF weighted geometric (t-AFWG) operators. Key properties such as idempotency, monotonicity, and boundedness of these operators are thoroughly examined. Furthermore, distance measures are formulated alongside their essential characteristics and special cases. To address multi-criteria group decision-making (MCGDM) problems under t-AF environment with unknown weight information, the tomada de decisao interativa multicriterio (TODIM) method is integrated with the criteria importance through an intercriteria correlation (CRITIC) approach. Finally, the proposed methodologies are validated through a case study on selecting the optimal gate security system, demonstrating their effectiveness and applicability in real-world scenarios.
- t-arbicular fuzzy set,
- distance measure,
- CRITIC,
- decision-making,
- TODIM method
Citation: Jawad Ali, Ioan-Lucian Popa. TODIM method with unknown weights under t-arbicular fuzzy environment for optimal gate security system selection[J]. AIMS Mathematics, 2025, 10(6): 13941-13973. doi: 10.3934/math.2025627

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Abstract

This study introduces the t-arbicular fuzzy (t-AF) set, an extension of the t-spherical fuzzy set, to enhance decision-making in complex environments. The research focuses on the theoretical foundation of the t-AF set, encompassing the development of algebraic operations and comparison rules. In addition, we propose novel aggregation operators (AOs), including the t-AF weighted average (t-AFWA) and t-AF weighted geometric (t-AFWG) operators. Key properties such as idempotency, monotonicity, and boundedness of these operators are thoroughly examined. Furthermore, distance measures are formulated alongside their essential characteristics and special cases. To address multi-criteria group decision-making (MCGDM) problems under t-AF environment with unknown weight information, the tomada de decisao interativa multicriterio (TODIM) method is integrated with the criteria importance through an intercriteria correlation (CRITIC) approach. Finally, the proposed methodologies are validated through a case study on selecting the optimal gate security system, demonstrating their effectiveness and applicability in real-world scenarios.

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