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<p>This study explores an innovative application of the analytical hierarchy process (AHP) within the multi-criteria decision-making (MCDM) technique. It focuses on the factors prompting career satisfaction in sports participation. As the importance of physical education and traditional sports in promoting complete development continues to increase, the need for systematic strategies becomes paramount. The MCDM approach based on Pythagorean fuzzy set (PyFS) helps as an effective tool for assessing the best alternatives among several choices. AHP helps with pairwise comparisons and assesses the relative importance of each criterion, enabling decision-makers to identify the most suitable option. The PyFS model provides a more advanced version of the fuzzy set, allowing for the meaning of both the degree of membership (DoM) and the degree of non-membership (DoNM) within the interval of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_5558_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left[ {0,1} \right]\)</EquationSource> </InlineEquation>. In this, we proposed some new aggregation operators (AOs) of Sugeno-Weber t-norm (TNM) and t-conorm (TCNM) based on PyFS, which are Pythagorean fuzzy Sugeno-Weber weighted averaging (PyFSWWA) and Pythagorean fuzzy Sugeno-Weber weighted geometric (PyFSWWG) operators. Also, we proposed a model of AHP to calculate the weight vector for criteria. We present the MCDM algorithm for AHP and the derived AOs, offering solutions to practical numerical examples and identifying optimal sports options that improve career happiness. In the case study, take four alternatives: Football, Swimming, Tennis, and Golf, based on physical health, mental health, character development, and discipline. When we use our proposed AOs to select the best alternatives. Tennis <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_5558_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\upbeta}_{2}\)</EquationSource> </InlineEquation> is the best alternative. To highlight the significance of the established model, we perform a comparative analysis with existing methods, concluding with a discussion of the key findings.</p>

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A Pythagorean fuzzy MCDM model for evaluating career happiness in sports by selecting a suitable sport

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  • 发表日期：

    2025年7月1日

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  • JiaYan Zhu,
  • Zeng Jiao

摘要

This study explores an innovative application of the analytical hierarchy process (AHP) within the multi-criteria decision-making (MCDM) technique. It focuses on the factors prompting career satisfaction in sports participation. As the importance of physical education and traditional sports in promoting complete development continues to increase, the need for systematic strategies becomes paramount. The MCDM approach based on Pythagorean fuzzy set (PyFS) helps as an effective tool for assessing the best alternatives among several choices. AHP helps with pairwise comparisons and assesses the relative importance of each criterion, enabling decision-makers to identify the most suitable option. The PyFS model provides a more advanced version of the fuzzy set, allowing for the meaning of both the degree of membership (DoM) and the degree of non-membership (DoNM) within the interval of \(\left[ {0,1} \right]\) . In this, we proposed some new aggregation operators (AOs) of Sugeno-Weber t-norm (TNM) and t-conorm (TCNM) based on PyFS, which are Pythagorean fuzzy Sugeno-Weber weighted averaging (PyFSWWA) and Pythagorean fuzzy Sugeno-Weber weighted geometric (PyFSWWG) operators. Also, we proposed a model of AHP to calculate the weight vector for criteria. We present the MCDM algorithm for AHP and the derived AOs, offering solutions to practical numerical examples and identifying optimal sports options that improve career happiness. In the case study, take four alternatives: Football, Swimming, Tennis, and Golf, based on physical health, mental health, character development, and discipline. When we use our proposed AOs to select the best alternatives. Tennis \({\upbeta}_{2}\) is the best alternative. To highlight the significance of the established model, we perform a comparative analysis with existing methods, concluding with a discussion of the key findings.