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AIMS Mathematics

2025, Volume 10, Issue 4: 8707-8720. doi: 10.3934/math.2025399
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Hamming distance-based knowledge measure and entropy for interval-valued Pythagorean fuzzy sets

  • College of Mathematical Sciences, Bohai University, Jinzhou 121000, China
  • Received: 06 January 2025 Revised: 20 March 2025 Accepted: 01 April 2025 Published: 15 April 2025

  • MSC : 03E72

  • The development of knowledge measures and uncertainty measures for constructing interval-valued Pythagorean fuzzy sets (IVPFS) have garnered significant attention in recent years. Nevertheless, existing uncertainty measures predominantly depend on entropy-based approaches, which exhibit limitations in effectively characterizing the knowledge inherent in interval intuitionistic fuzzy sets. This study extends the axiomatic framework of knowledge measures for fuzzy sets by introducing a novel distance-based knowledge measure function. The proposed measure is rigorously validated through comprehensive mathematical analysis and supported by extensive numerical examples. Furthermore, this research extends the entropy properties from interval-valued intuitionistic fuzzy sets to their Pythagorean counterparts while providing rigorous proofs of their compliance with axiomatic definitions. To demonstrate practical applicability, the proposed entropy measure is implemented in multi-attribute group decision-making scenarios involving unknown interval-valued Pythagorean fuzzy information. Experimental results substantiate both the validity and practical utility of the proposed measures.

    Citation: Li Li, Xin Wang. Hamming distance-based knowledge measure and entropy for interval-valued Pythagorean fuzzy sets[J]. AIMS Mathematics, 2025, 10(4): 8707-8720. doi: 10.3934/math.2025399

    Related Papers:

  • The development of knowledge measures and uncertainty measures for constructing interval-valued Pythagorean fuzzy sets (IVPFS) have garnered significant attention in recent years. Nevertheless, existing uncertainty measures predominantly depend on entropy-based approaches, which exhibit limitations in effectively characterizing the knowledge inherent in interval intuitionistic fuzzy sets. This study extends the axiomatic framework of knowledge measures for fuzzy sets by introducing a novel distance-based knowledge measure function. The proposed measure is rigorously validated through comprehensive mathematical analysis and supported by extensive numerical examples. Furthermore, this research extends the entropy properties from interval-valued intuitionistic fuzzy sets to their Pythagorean counterparts while providing rigorous proofs of their compliance with axiomatic definitions. To demonstrate practical applicability, the proposed entropy measure is implemented in multi-attribute group decision-making scenarios involving unknown interval-valued Pythagorean fuzzy information. Experimental results substantiate both the validity and practical utility of the proposed measures.



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