<p>In this study, we develop a novel three-way decision method considering decision-makers’ psychological behavior based on set pair analysis. First, we propose an adjustable excellent state set, and combine it with the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(O-\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo>-</mo> <mi>α</mi> </mrow> </math></EquationSource> </InlineEquation> neighborhood to introduce a new method for calculating conditional probabilities. Second, leveraging regret theory, we introduce a variable to moderate the degree of decision-makers’ regret–joy, characterizing the impact of decision-makers’ psychological behavior on decision outcomes. Building upon this, we construct a new relative utility function and integrate it with prospect theory to develop a three-way decision method suitable for fuzzy incomplete information systems, incomplete information systems, and complete information systems. Comparative analysis with existing methods demonstrates the rationality and superiority of our approach. Sensitivity analysis confirms the stability of the method.</p>

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A Prospect–Regret-Theory-Based Three-Way Decision Approach with the \(O-\alpha \) Neighborhood Under Fuzzy Incomplete Information Systems

  • Jiaxin Song,
  • Haidong Zhang,
  • Yanping He

摘要

In this study, we develop a novel three-way decision method considering decision-makers’ psychological behavior based on set pair analysis. First, we propose an adjustable excellent state set, and combine it with the \(O-\alpha \) O - α neighborhood to introduce a new method for calculating conditional probabilities. Second, leveraging regret theory, we introduce a variable to moderate the degree of decision-makers’ regret–joy, characterizing the impact of decision-makers’ psychological behavior on decision outcomes. Building upon this, we construct a new relative utility function and integrate it with prospect theory to develop a three-way decision method suitable for fuzzy incomplete information systems, incomplete information systems, and complete information systems. Comparative analysis with existing methods demonstrates the rationality and superiority of our approach. Sensitivity analysis confirms the stability of the method.