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This study introduces an innovative Advanced Pythagorean Fuzzy Hamacher Weighted Geometric (APyFHWG) operator. The APyFHWG operator addresses inherent limitations in several existing geometric operators (GOs), including the Pythagorean Fuzzy Dombi weighted Geometric (PyFDWG) operator, Pythagorean Fuzzy Hamacher Power Weighted Geometric (PyFHPWG) operator, Symmetric Pythagorean Fuzzy Weighted Geometric (SPyFWG) operator, Pythagorean Fuzzy Hamacher Prioritized weighted Geometric (PyFHPrWG) operator, and Pythagorean Fuzzy Interactive Hamacher Power Weighted Geometric (PyFIHPWG) operator. These shortcomings primarily involve the indeterminacy of aggregated results in specific scenarios when a Pythagorean fuzzy number contains zero membership grade and its corresponding weight component equals zero. Furthermore, the aggregated result remains indeterminate when the indeterminacy degree of a component Pythagorean fuzzy number reaches zero alongside its corresponding weight component. Additionally, MCDM methods utilizing these GOs struggle to discern the ranking order of alternatives. The proposed APyFHWG operator effectively mitigates these drawbacks. Finally, we present a case study focused on the selection of green suppliers within the pharmaceutical industry in India as a practical application of our methodology.

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Novel Pythagorean Fuzzy Hamacher Aggregation Operator and Its Application to Green Supplier Selection in Pharmaceutical Industry

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  • 发表日期：

    2025年

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  • Tapas Kumar Paul,
  • Madhumangal Pal

摘要

This study introduces an innovative Advanced Pythagorean Fuzzy Hamacher Weighted Geometric (APyFHWG) operator. The APyFHWG operator addresses inherent limitations in several existing geometric operators (GOs), including the Pythagorean Fuzzy Dombi weighted Geometric (PyFDWG) operator, Pythagorean Fuzzy Hamacher Power Weighted Geometric (PyFHPWG) operator, Symmetric Pythagorean Fuzzy Weighted Geometric (SPyFWG) operator, Pythagorean Fuzzy Hamacher Prioritized weighted Geometric (PyFHPrWG) operator, and Pythagorean Fuzzy Interactive Hamacher Power Weighted Geometric (PyFIHPWG) operator. These shortcomings primarily involve the indeterminacy of aggregated results in specific scenarios when a Pythagorean fuzzy number contains zero membership grade and its corresponding weight component equals zero. Furthermore, the aggregated result remains indeterminate when the indeterminacy degree of a component Pythagorean fuzzy number reaches zero alongside its corresponding weight component. Additionally, MCDM methods utilizing these GOs struggle to discern the ranking order of alternatives. The proposed APyFHWG operator effectively mitigates these drawbacks. Finally, we present a case study focused on the selection of green suppliers within the pharmaceutical industry in India as a practical application of our methodology.