<p>Green supplier selection is a critical multi-criteria decision making (MCDM) problem in green supply chain management, requiring evaluation of multiple suppliers under economic, environmental, and social criteria while handling vague, imprecise, and conflicting expert judgments. Existing fuzzy-based MCDM approaches often have limitations in representing uncertainty flexibly, as they rely on fixed boundaries for membership and non-membership degrees, which may constrain decision-makers expressive capability and reduce robustness in complex environments. To address these challenges, this study proposes a novel MCDM framework based on circular p,q-quasirung orthopair fuzzy sets (C<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$pq$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">pq</mi> </mrow> </math></EquationSource> </InlineEquation>QOFSs), which extend p,q-quasirung orthopair and circular q-rung orthopair fuzzy sets by introducing circular regions with adjustable centers and radii. This enables more flexible and realistic modeling of uncertainty. We develop fundamental set-theoretic operations, score and accuracy functions, distance measures, and Sugeno–Weber weighted aggregation operators for C<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$pq$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">pq</mi> </mrow> </math></EquationSource> </InlineEquation>QOFSs, which are then employed to construct the proposed multi-criteria group decision-making (MCGDM) framework. The framework is applied to a green supplier selection problem evaluated by five focus groups, led by a panel of five field experts with extensive knowledge and experience in environmental sciences, supply chain management, logistics, procurement, sustainability, and social welfare, using four critical sustainability-related criteria. The results yield a clear ranking of alternatives that can well identify the most suitable supplier. Sensitivity analysis further validates the robustness of the ranking. In addition, a comparative analysis with existing fuzzy sets and their various extensions demonstrates the superiority and effectiveness of the proposed approach. Compared to more complex extensions such as neutrosophic sets, the C<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$pq$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">pq</mi> </mrow> </math></EquationSource> </InlineEquation>QOFS-based framework provides sufficient flexibility and expressive power while maintaining mathematical tractability and ease of implementation. The results confirm that the proposed approach is a robust and practical tool for solving complex MCDM problems under uncertainty.</p>

On circular p,q-quasirung orthopair fuzzy sets with their aggregation operators and application to green supplier selection

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2026年2月18日

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Mehboob Ali,
Yasir Akhtar,
Muhammad Rahim,
Miin-Shen Yang

摘要

Green supplier selection is a critical multi-criteria decision making (MCDM) problem in green supply chain management, requiring evaluation of multiple suppliers under economic, environmental, and social criteria while handling vague, imprecise, and conflicting expert judgments. Existing fuzzy-based MCDM approaches often have limitations in representing uncertainty flexibly, as they rely on fixed boundaries for membership and non-membership degrees, which may constrain decision-makers expressive capability and reduce robustness in complex environments. To address these challenges, this study proposes a novel MCDM framework based on circular p,q-quasirung orthopair fuzzy sets (C $pq$ $pq$ QOFSs), which extend p,q-quasirung orthopair and circular q-rung orthopair fuzzy sets by introducing circular regions with adjustable centers and radii. This enables more flexible and realistic modeling of uncertainty. We develop fundamental set-theoretic operations, score and accuracy functions, distance measures, and Sugeno–Weber weighted aggregation operators for C $pq$ $pq$ QOFSs, which are then employed to construct the proposed multi-criteria group decision-making (MCGDM) framework. The framework is applied to a green supplier selection problem evaluated by five focus groups, led by a panel of five field experts with extensive knowledge and experience in environmental sciences, supply chain management, logistics, procurement, sustainability, and social welfare, using four critical sustainability-related criteria. The results yield a clear ranking of alternatives that can well identify the most suitable supplier. Sensitivity analysis further validates the robustness of the ranking. In addition, a comparative analysis with existing fuzzy sets and their various extensions demonstrates the superiority and effectiveness of the proposed approach. Compared to more complex extensions such as neutrosophic sets, the C $pq$ $pq$ QOFS-based framework provides sufficient flexibility and expressive power while maintaining mathematical tractability and ease of implementation. The results confirm that the proposed approach is a robust and practical tool for solving complex MCDM problems under uncertainty.