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<p>In decision-making environments characterized by uncertainty and ambiguous information, effectively reducing decision risk presents a significant challenge. The three-way decision provides a structured approach to addressing ambiguity by offering three choices: accept, reject, and defer. However, finer characterization of ambiguity and consideration of psychological factors remain insufficient. Intuitionistic fuzzy sets, defined by membership, non-membership, and hesitation degrees, enable a more nuanced representation of fuzzy states. Prospect theory, conversely, reveals psychological preferences in risk decision-making. This paper integrates three key elements: the three-way decision-making structure, the descriptive power of intuitionistic fuzzy sets, and the behavioral insights of prospect theory. It aims to develop an integrated fusion framework that can more efficiently manage complex and ambiguous information, thereby reducing the potential risks associated with decision-making processes. First, we propose a novel intuitionistic fuzzy similarity metric, which is utilized to assess the degree of similarity among different decision options. This measure is then used to derive similarity classes and support a new approach for calculating conditional probabilities. Secondly, we introduce a relative utility function grounded in prospect theory, which is subsequently integrated with conditional probability to form a novel three-way decision-making framework. The proposed approach not only enables effective classification and ranking but also better aligns with the psychological dynamics of decision-makers. Finally, we test the method on a big data case of air quality index and contrast with other decision-making methods, verifying the effectiveness, universality, and superiority of the method. Additionally, we perform sensitivity analyses on the parameter <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\varphi\)</EquationSource></InlineEquation>, which affects the conditional probability, as well as on the parameters <i>L</i> and <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\xi\)</EquationSource></InlineEquation>, which influence the utility function, thereby demonstrating the robustness of the approach.</p>

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A three-way decision-making method integrating prospect theory and intuitionistic fuzzy similarity for air quality index big data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月5日

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  • Shiliang Lyu,
  • Zhuoma Dawa,
  • Haidong Zhang

摘要

In decision-making environments characterized by uncertainty and ambiguous information, effectively reducing decision risk presents a significant challenge. The three-way decision provides a structured approach to addressing ambiguity by offering three choices: accept, reject, and defer. However, finer characterization of ambiguity and consideration of psychological factors remain insufficient. Intuitionistic fuzzy sets, defined by membership, non-membership, and hesitation degrees, enable a more nuanced representation of fuzzy states. Prospect theory, conversely, reveals psychological preferences in risk decision-making. This paper integrates three key elements: the three-way decision-making structure, the descriptive power of intuitionistic fuzzy sets, and the behavioral insights of prospect theory. It aims to develop an integrated fusion framework that can more efficiently manage complex and ambiguous information, thereby reducing the potential risks associated with decision-making processes. First, we propose a novel intuitionistic fuzzy similarity metric, which is utilized to assess the degree of similarity among different decision options. This measure is then used to derive similarity classes and support a new approach for calculating conditional probabilities. Secondly, we introduce a relative utility function grounded in prospect theory, which is subsequently integrated with conditional probability to form a novel three-way decision-making framework. The proposed approach not only enables effective classification and ranking but also better aligns with the psychological dynamics of decision-makers. Finally, we test the method on a big data case of air quality index and contrast with other decision-making methods, verifying the effectiveness, universality, and superiority of the method. Additionally, we perform sensitivity analyses on the parameter \(\varphi\), which affects the conditional probability, as well as on the parameters L and \(\xi\), which influence the utility function, thereby demonstrating the robustness of the approach.