A new score function of interval-valued intuitionistic fuzzy values based on prospect theory

Benting Wan; Jun Wan; Juan Zhang; Jin Xie; Youyu Cheng; Wenzhong Peng; Benting Wan; Jun Wan; Juan Zhang; Jin Xie; Youyu Cheng; Wenzhong Peng

doi:10.3934/math.20251219

AIMS Mathematics

2025, Volume 10, Issue 11: 27718-27754. doi: 10.3934/math.20251219

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Research article Topical Sections

A new score function of interval-valued intuitionistic fuzzy values based on prospect theory

1.
School of Software and IoT Engineering, Jiangxi University of Finance and Economics, Nanchang 330013, China
2.
Jiujiang Polytechnic University of Science and Technology, Gongqing City, Jiangxi 332020, China

Received: 16 September 2025 Revised: 05 November 2025 Accepted: 18 November 2025 Published: 27 November 2025
MSC : 03E27, 90B50

As a fundamental tool for interval-valued intuitionistic fuzzy sets (IVIFSs), the score function (SF) plays a pivotal role in quantifying interval-valued intuitionistic fuzzy values (IVIFVs) and facilitating their comparative analysis. However, a notable limitation of existing SFs is their potential to assign identical scores to distinct IVIFVs, thereby compromising the discrimination capability. To address this challenge, this study introduces IVIFS-SF, a novel score function grounded in prospect theory, and proposes two innovative assessment methodologies. First, we employed prospect theory to develop an interval-valued evaluation method (IVEM), which converts the interval into a crisp number. Second, using IVEM, we developed the new score function IVIFS-SF and present its properties. Third, we put forward pass rate and variance as metrics to analyze and compare SFs. Rigorous comparative analysis demonstrated that IVIFS-SF achieves superior performance in both pass rate and variance metrics when benchmarked against existing state-of-the-art SFs. Furthermore, sensitivity analysis confirmed the robustness of IVIFS-SF across the parameter spectrum of prospect theory. Empirical case studies revealed that while IVIFS-SF identifies the same optimal alternative as competing SFs, it exhibits the highest variance among them, suggesting enhanced discriminative power.
- prospect theory,
- IVIFS,
- interval-valued evaluation,
- score function,
- IVIFV
Citation: Benting Wan, Jun Wan, Juan Zhang, Jin Xie, Youyu Cheng, Wenzhong Peng. A new score function of interval-valued intuitionistic fuzzy values based on prospect theory[J]. AIMS Mathematics, 2025, 10(11): 27718-27754. doi: 10.3934/math.20251219

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Abstract

As a fundamental tool for interval-valued intuitionistic fuzzy sets (IVIFSs), the score function (SF) plays a pivotal role in quantifying interval-valued intuitionistic fuzzy values (IVIFVs) and facilitating their comparative analysis. However, a notable limitation of existing SFs is their potential to assign identical scores to distinct IVIFVs, thereby compromising the discrimination capability. To address this challenge, this study introduces IVIFS-SF, a novel score function grounded in prospect theory, and proposes two innovative assessment methodologies. First, we employed prospect theory to develop an interval-valued evaluation method (IVEM), which converts the interval into a crisp number. Second, using IVEM, we developed the new score function IVIFS-SF and present its properties. Third, we put forward pass rate and variance as metrics to analyze and compare SFs. Rigorous comparative analysis demonstrated that IVIFS-SF achieves superior performance in both pass rate and variance metrics when benchmarked against existing state-of-the-art SFs. Furthermore, sensitivity analysis confirmed the robustness of IVIFS-SF across the parameter spectrum of prospect theory. Empirical case studies revealed that while IVIFS-SF identifies the same optimal alternative as competing SFs, it exhibits the highest variance among them, suggesting enhanced discriminative power.

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