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<p>Atanassov introduced Intuitionistic Fuzzy Sets (IFSs) to more effectively capture vagueness and uncertainty than traditional Fuzzy Sets (FSs). One of the key challenges in fuzzy systems is quantifying uncertainty within a fuzzy set, which is typically measured using entropy. This study proposes a novel entropy measure for IFSs, based on an axiomatic definition. To establish the need for this measure, we first review existing entropy measures for IFSs and highlight their limitations. Numerical comparisons are then provided to demonstrate the superior performance of the proposed measure. Furthermore, we extend this entropy measure to develop the Intuitionistic Fuzzy Technique for Order Preference by Similarity to an Ideal Solution (IF-TOPSIS), aimed at solving complex multi-criteria decision-making (MCDM) problems. Numerical examples and comparative analyses are presented to validate the accuracy, effectiveness, and practical applicability of the proposed method in real-world decision-making scenarios.</p>

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Intuitionistic fuzzy entropy and its application to hydro power plant site selection with multicriteria decision making

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Zahid Hussain,
  • Nadeem Abbas,
  • Rashid Hussain

摘要

Atanassov introduced Intuitionistic Fuzzy Sets (IFSs) to more effectively capture vagueness and uncertainty than traditional Fuzzy Sets (FSs). One of the key challenges in fuzzy systems is quantifying uncertainty within a fuzzy set, which is typically measured using entropy. This study proposes a novel entropy measure for IFSs, based on an axiomatic definition. To establish the need for this measure, we first review existing entropy measures for IFSs and highlight their limitations. Numerical comparisons are then provided to demonstrate the superior performance of the proposed measure. Furthermore, we extend this entropy measure to develop the Intuitionistic Fuzzy Technique for Order Preference by Similarity to an Ideal Solution (IF-TOPSIS), aimed at solving complex multi-criteria decision-making (MCDM) problems. Numerical examples and comparative analyses are presented to validate the accuracy, effectiveness, and practical applicability of the proposed method in real-world decision-making scenarios.