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<p>Distance measure has become an intrinsic mathematical tool for decision-making. A decision may be optimistic, moderate or pessimistic, depending upon the decision-maker’s viewpoint. This study addresses these different aspects of decision-making in the context of distance measure in the Pythagorean fuzzy environment. It has been found that there exists no distance measure in the Pythagorean fuzzy literature that adopts a pessimistic viewpoint. Hence, this study proposes one such distance measure and illustrates the necessity to address a problem from a pessimistic perspective of information through a medical problem. Various numerical examples and comparative analysis validate the uniqueness and superiority of the proposed measure. Its applicability to real-life issues is demonstrated through a case study on the Global Gender Gap report of 2024 and various other decision-making problems. The statistical analysis of the multi-criteria decision-making problems establish consistency and reliability of results produced by the new distance measure. Moreover, the sensitivity analysis demonstrates the robustness of decisions by the proposed measure.</p>

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Distance measure on Pythagorean fuzzy sets from a pessimistic viewpoint and its application to decision-making problems

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Chinmayee Devi,
  • Rituparna Chutia,
  • Brindaban Gohain

摘要

Distance measure has become an intrinsic mathematical tool for decision-making. A decision may be optimistic, moderate or pessimistic, depending upon the decision-maker’s viewpoint. This study addresses these different aspects of decision-making in the context of distance measure in the Pythagorean fuzzy environment. It has been found that there exists no distance measure in the Pythagorean fuzzy literature that adopts a pessimistic viewpoint. Hence, this study proposes one such distance measure and illustrates the necessity to address a problem from a pessimistic perspective of information through a medical problem. Various numerical examples and comparative analysis validate the uniqueness and superiority of the proposed measure. Its applicability to real-life issues is demonstrated through a case study on the Global Gender Gap report of 2024 and various other decision-making problems. The statistical analysis of the multi-criteria decision-making problems establish consistency and reliability of results produced by the new distance measure. Moreover, the sensitivity analysis demonstrates the robustness of decisions by the proposed measure.