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Optimization-Based Three-Way Decisions With Interval-Valued Intuitionistic Fuzzy Information.

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    This study introduces interval-valued intuitionistic fuzzy sets (IVIFSs) into decision-theoretic rough sets (DTRSs) for enhanced three-way decisions. The new optimization approach effectively handles uncertainty and risk, offering distinct advantages over existing methods.

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    Area of Science:

    • Decision Sciences
    • Fuzzy Set Theory
    • Artificial Intelligence

    Background:

    • Interval-valued intuitionistic fuzzy sets (IVIFSs) offer robust uncertainty evaluation.
    • Decision-theoretic rough sets (DTRSs) provide a framework for decision making under uncertainty.
    • Existing models for three-way decisions have limitations in handling complex uncertainty.

    Purpose of the Study:

    • To propose an optimization-based approach for interval-valued intuitionistic fuzzy three-way decisions.
    • To integrate IVIFSs into the loss functions of DTRSs.
    • To develop a novel method that addresses limitations in current uncertainty and risk evaluation models.

    Main Methods:

    • Constructed a concise linear programming model for threshold pair determination, mathematically equivalent to DTRSs under KKT conditions.
    • Extended the model using IVIFSs for loss functions, analyzing relationships via similarity and multiple score function-based ranking methods.
    • Developed extended models using two ranking methods, proving the existence and uniqueness of optimal solutions.

    Main Results:

    • An optimization-based algorithm for three-way decisions in an interval-valued intuitionistic fuzzy environment was developed.
    • The proposed method demonstrated mathematical equivalence to existing DTRSs and models.
    • The approach offers three key advantages over the latest existing methods, as shown in an illustrative example.

    Conclusions:

    • The proposed optimization-based approach effectively integrates IVIFSs into DTRSs for three-way decisions.
    • The method provides a unique and existing optimal solution for decision-making under uncertainty.
    • This novel approach offers significant advantages in evaluating uncertainty and risk compared to existing techniques.