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Interactive group decision making method based on probabilistic hesitant Pythagorean fuzzy information

Gang Sun1, Weican Hua2, Guijun Wang2

  • 1School of Science, Hunan Institute of Technology, Hengyang, 421002 Hunan China.

Applied Intelligence (Dordrecht, Netherlands)
|July 20, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new decision-making method using probabilistic hesitant Pythagorean fuzzy sets (PrHPFS) to improve group consensus. The approach enhances expert evaluations by incorporating probability, leading to more accurate and consistent group preferences.

Keywords:
Degree of similarityHamming distance measureInteractive group decision makingProbabilistic hesitant Pythagorean fuzzy number (PrHPFN)Pythagorean fuzzy number (PFN)

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Area of Science:

  • Decision Sciences
  • Fuzzy Set Theory
  • Information Fusion

Background:

  • Interactive group evaluation aims for consensus by adjusting expert weights.
  • Hesitant Pythagorean fuzzy sets (HPFS) represent uncertainty but lack probabilistic information.
  • Existing methods may not fully capture complex expert decision-making under uncertainty.

Purpose of the Study:

  • To introduce probabilistic hesitant Pythagorean fuzzy sets (PrHPFS) as a generalization of HPFS and Pythagorean fuzzy sets (PFS).
  • To develop novel score and accuracy functions for probabilistic hesitant Pythagorean fuzzy numbers (PrHPFNs).
  • To design an interactive group decision-making method based on PrHPFS for achieving consensus.

Main Methods:

  • Reviewed basic definitions and operations for PrHPFNs.
  • Proposed score and accuracy functions within the PrHPFNs environment.
  • Introduced Hamming distance, weighted distance, and similarity measures for PrHPFMs.
  • Developed an interactive group decision-making algorithm using PrHPFMs and similarity measures.

Main Results:

  • Established foundational concepts and operations for PrHPFS.
  • Quantified uncertainty and preference using new score and accuracy functions.
  • Demonstrated the effectiveness of the proposed interactive group decision-making method through an example.
  • Achieved consistent consensus evaluation by mitigating expert hesitation.

Conclusions:

  • PrHPFS offers a more comprehensive representation of expert decision information compared to HPFS and PFS.
  • The developed distance and similarity measures are effective in the PrHPFS space.
  • The proposed interactive group decision-making method successfully facilitates consensus and overcomes expert hesitation.