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<p>The rapid expansion of renewable energy technologies has intensified the need for reliable decision-making tools for solar panel selection, a problem characterized by multiple technical, economic, and environmental criteria evaluated under high uncertainty. Conventional fuzzy frameworks, including intuitionistic fuzzy sets and their extensions, provide valuable modeling capabilities but remain limited in handling extreme or highly confident assessments, particularly when membership or non-membership degrees attain boundary values. Moreover, existing models often impose restrictive dependencies between membership and non-membership information, which may distort expert judgments. To address these limitations, this study proposes a novel decision-making framework based on p,q-fractional fuzzy sets (p,q-FFSs), which significantly enlarges the admissible information domain while preserving mathematical consistency. Fundamental operational laws, along with score and accuracy functions, are established for p,q-fractional fuzzy (p,q-FF) numbers. Building on this foundation, two aggregation operators (AOs) are developed and integrated into a multi-criteria group decision-making (MCGDM) methodology. The applicability and effectiveness of the proposed approach are demonstrated through a solar panel selection case study involving multiple experts, criteria, and alternatives. Sensitivity analysis with respect to parameters <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation> confirms the robustness and stability of the ranking results, while comparative analysis with several well-established fuzzy and fractional fuzzy decision-making methods shows improved expressive capability, flexibility, and consistency. The results indicate that the proposed p,q-fractional fuzzy framework provides a more realistic and reliable tool for complex decision-making problems in renewable energy planning and other uncertainty-driven application domains.</p>

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On \(p,q\)–Fractional Fuzzy Sets with Application in Solar Panel Selection

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月28日

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  • Zhifang Han,
  • Muhammad Rahim,
  • Yasir Akhtar,
  • Miin-Shen Yang

摘要

The rapid expansion of renewable energy technologies has intensified the need for reliable decision-making tools for solar panel selection, a problem characterized by multiple technical, economic, and environmental criteria evaluated under high uncertainty. Conventional fuzzy frameworks, including intuitionistic fuzzy sets and their extensions, provide valuable modeling capabilities but remain limited in handling extreme or highly confident assessments, particularly when membership or non-membership degrees attain boundary values. Moreover, existing models often impose restrictive dependencies between membership and non-membership information, which may distort expert judgments. To address these limitations, this study proposes a novel decision-making framework based on p,q-fractional fuzzy sets (p,q-FFSs), which significantly enlarges the admissible information domain while preserving mathematical consistency. Fundamental operational laws, along with score and accuracy functions, are established for p,q-fractional fuzzy (p,q-FF) numbers. Building on this foundation, two aggregation operators (AOs) are developed and integrated into a multi-criteria group decision-making (MCGDM) methodology. The applicability and effectiveness of the proposed approach are demonstrated through a solar panel selection case study involving multiple experts, criteria, and alternatives. Sensitivity analysis with respect to parameters \(p\) and \(q\) confirms the robustness and stability of the ranking results, while comparative analysis with several well-established fuzzy and fractional fuzzy decision-making methods shows improved expressive capability, flexibility, and consistency. The results indicate that the proposed p,q-fractional fuzzy framework provides a more realistic and reliable tool for complex decision-making problems in renewable energy planning and other uncertainty-driven application domains.