Randić energies in decision making for human trafficking by interval-valued T-spherical fuzzy Hamacher graphs

Ali Ahmad; Humera Rashid; Hamdan Alshehri; Muhammad Kamran Jamil; Haitham Assiri; Ali Ahmad; Humera Rashid; Hamdan Alshehri; Muhammad Kamran Jamil; Haitham Assiri

doi:10.3934/math.2025446

AIMS Mathematics

2025, Volume 10, Issue 4: 9697-9747. doi: 10.3934/math.2025446

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Research article

Randić energies in decision making for human trafficking by interval-valued T-spherical fuzzy Hamacher graphs

1.
Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
2.
Department of Mathematics, Riphah International University, Lahore Campus, Pakistan

Received: 15 February 2025 Revised: 15 April 2025 Accepted: 18 April 2025 Published: 25 April 2025
MSC : 05C12, 05C72, 90C70

The interval-valued ($ IV $) T-spherical fuzzy set $ (IVTSFS) $ appears to be more effective and practical in dealing with uncertainty and ambiguity while dealing with various decision-making ($ DM $) problems than other fuzzy sets, for example, the q-rung ortho-pair fuzzy set, T-spherical fuzzy set, and picture fuzzy set. In real-life problems, where intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, or interval-valued picture fuzzy sets give unsatisfactory results, the $ IVTSFS $ is a mathematical model that is used to deal with such problems where these method fails, and one can handle it efficiently by using $ IVTSFS. $ If there is a different framework that has a base of four opinions — yes, no, abstains, and refusal — the $ IVTSFS $ looks to be the most beneficial, and it is also proven to be so. In this article, an idea of interval-valued T-spherical fuzzy Hamacher graphs $ (IVTSFHGs) $ is proposed, which is based on the Hamacher t-norm ($ TN $) and Hamacher t-conorm ($ TCN $). It provides enhanced discrimination and flexibility in uncertain environments by capturing a broader spectrum of hesitancy and indeterminacy, which other fuzzy models like interval-valued intuitionistic fuzzy set ($ IVIFS $) or picture fuzzy set ($ PFS $) may overlook. This article aims to examine the energy associated with the splitting of $ IVTSFHGs, $ as well as the energy related to shadow $ IVTSFHGs. $ Moreover, the Randić energy of $ IVTSFHGs $ was presented, and an in-depth analysis of its essential outcomes was conducted. Additionally, this study introduces interval-valued T-spherical fuzzy Hamacher digraphs $ (IVTSFHDGs) $ and explores their diverse outcomes. An algorithm involving $ IVTSFHDGs $ was also studied, which is used to propose energies of $ IVTSFHGs $ in $ DM $, problems, and Hamacher aggregation operators. To validate the proposed results, a comparative study is conducted.
- Randić energies,
- human trafficking,
- interval-valued T-spherical fuzzy Hamacher graphs,
- fuzzy graph
Citation: Ali Ahmad, Humera Rashid, Hamdan Alshehri, Muhammad Kamran Jamil, Haitham Assiri. Randić energies in decision making for human trafficking by interval-valued T-spherical fuzzy Hamacher graphs[J]. AIMS Mathematics, 2025, 10(4): 9697-9747. doi: 10.3934/math.2025446

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Abstract

The interval-valued ($ IV $) T-spherical fuzzy set $ (IVTSFS) $ appears to be more effective and practical in dealing with uncertainty and ambiguity while dealing with various decision-making ($ DM $) problems than other fuzzy sets, for example, the q-rung ortho-pair fuzzy set, T-spherical fuzzy set, and picture fuzzy set. In real-life problems, where intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, or interval-valued picture fuzzy sets give unsatisfactory results, the $ IVTSFS $ is a mathematical model that is used to deal with such problems where these method fails, and one can handle it efficiently by using $ IVTSFS. $ If there is a different framework that has a base of four opinions — yes, no, abstains, and refusal — the $ IVTSFS $ looks to be the most beneficial, and it is also proven to be so. In this article, an idea of interval-valued T-spherical fuzzy Hamacher graphs $ (IVTSFHGs) $ is proposed, which is based on the Hamacher t-norm ($ TN $) and Hamacher t-conorm ($ TCN $). It provides enhanced discrimination and flexibility in uncertain environments by capturing a broader spectrum of hesitancy and indeterminacy, which other fuzzy models like interval-valued intuitionistic fuzzy set ($ IVIFS $) or picture fuzzy set ($ PFS $) may overlook. This article aims to examine the energy associated with the splitting of $ IVTSFHGs, $ as well as the energy related to shadow $ IVTSFHGs. $ Moreover, the Randić energy of $ IVTSFHGs $ was presented, and an in-depth analysis of its essential outcomes was conducted. Additionally, this study introduces interval-valued T-spherical fuzzy Hamacher digraphs $ (IVTSFHDGs) $ and explores their diverse outcomes. An algorithm involving $ IVTSFHDGs $ was also studied, which is used to propose energies of $ IVTSFHGs $ in $ DM $, problems, and Hamacher aggregation operators. To validate the proposed results, a comparative study is conducted.

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