<p>Physical education and traditional sports are gaining increasing importance for comprehensive development, making the systemic design of classrooms necessary. Well-designed physical education rooms encourage students to participate in both curricular and extracurricular activities. With a well-structured classroom, opportunities for various teaching methods are available, and everyone is encouraged to participate. The research presents a novel approach to applying the Analytical Hierarchy Process (AHP) within multi-criteria decision-making (MCDM) to design physical education classroom environments. The MCDM approach facilitates the successful evaluation of superior options among multiple alternatives. Through AHP processes, decision-makers can evaluate the importance of criteria by making pairwise comparisons until they identify the most suitable choice. The q-rung ortho pair fuzzy set (q-ROFS) framework extends fuzzy sets with a more sophisticated system that shows both the degree of membership (DoM) and degree of non-membership (DoNM) throughout the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_15015_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> interval with a large range. The Sugeno-Weber t-norm (TNM) and t-conorm (TCNM) play a significant role in modeling flexible fuzzy systems, offering more control over how fuzzy sets interact. Due to their adjustable parameters, they can easily aggregate complex information. We aimed to develop aggregation operators (AOs) based on the AHP, combined with Sugeno-Weber TNM and TCNM, known as q-rung orthopair fuzzy Sugeno-Weber weighted averaging (q-ROFSWWA) and q-rung orthopair fuzzy Sugeno-Weber weighted geometric (q-ROFSWWG) operators, to address current needs. Additionally, the paper describes an improved combined compromise solution (CCS) methodology to determine the precise ranking of alternatives. Then, we presented the MCDM algorithms of the developed q-ROFSWWA and COCOSO approach under AHP and q-ROFS information. Through practical examples, we rank the four different classes for physical education, including versatile equipment, integration of outdoor spaces, adaptable and versatile environments, and safety and comfort features. We apply our proposed theory to investigate four alternatives, and the obtained result is “integration of outdoor spaces.” To demonstrate the importance of the proposed approach, we conduct a comparative analysis to investigate authenticity and validation. Then, we provide a conclusion. The graphical abstract of the article is provided in Fig. 1.</p>

Assessment of classroom design for physical education using COCOSO algorithm and modified Sugeno Weber aggregation operators

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2025年9月1日

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Qiaoli Wei,
Junwei Yao,
Weitao Zheng

摘要

Physical education and traditional sports are gaining increasing importance for comprehensive development, making the systemic design of classrooms necessary. Well-designed physical education rooms encourage students to participate in both curricular and extracurricular activities. With a well-structured classroom, opportunities for various teaching methods are available, and everyone is encouraged to participate. The research presents a novel approach to applying the Analytical Hierarchy Process (AHP) within multi-criteria decision-making (MCDM) to design physical education classroom environments. The MCDM approach facilitates the successful evaluation of superior options among multiple alternatives. Through AHP processes, decision-makers can evaluate the importance of criteria by making pairwise comparisons until they identify the most suitable choice. The q-rung ortho pair fuzzy set (q-ROFS) framework extends fuzzy sets with a more sophisticated system that shows both the degree of membership (DoM) and degree of non-membership (DoNM) throughout the \(\left[0, 1\right]\) interval with a large range. The Sugeno-Weber t-norm (TNM) and t-conorm (TCNM) play a significant role in modeling flexible fuzzy systems, offering more control over how fuzzy sets interact. Due to their adjustable parameters, they can easily aggregate complex information. We aimed to develop aggregation operators (AOs) based on the AHP, combined with Sugeno-Weber TNM and TCNM, known as q-rung orthopair fuzzy Sugeno-Weber weighted averaging (q-ROFSWWA) and q-rung orthopair fuzzy Sugeno-Weber weighted geometric (q-ROFSWWG) operators, to address current needs. Additionally, the paper describes an improved combined compromise solution (CCS) methodology to determine the precise ranking of alternatives. Then, we presented the MCDM algorithms of the developed q-ROFSWWA and COCOSO approach under AHP and q-ROFS information. Through practical examples, we rank the four different classes for physical education, including versatile equipment, integration of outdoor spaces, adaptable and versatile environments, and safety and comfort features. We apply our proposed theory to investigate four alternatives, and the obtained result is “integration of outdoor spaces.” To demonstrate the importance of the proposed approach, we conduct a comparative analysis to investigate authenticity and validation. Then, we provide a conclusion. The graphical abstract of the article is provided in Fig. 1.