<p>With growing resource shortages and environmental concerns, countries are advancing green manufacturing and green product development. Evaluating green product conceptual design schemes (GPCDSs) is critical for green product innovation, this paper aims to establish a scientific evaluation model for GPCDSs. Firstly, the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-sphere Z-fuzzy numbers (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-SZFNs) are defined to describe the evaluation information. It is a combination of spherical Z-fuzzy numbers (SZFNs) and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-cuts, which retains the advantages of SZFNs in dealing with fuzziness and providing reliability constraints. Meanwhile, <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-cuts simplify the calculation process of SZFNs and reduce information loss. Then, an advantage degree formula is constructed for comparing <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-SZFNs to define gain and loss functions. Secondly, the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>-fuzzy measure, which is a non-additive measure with simple calculation process, is introduced into the Shapley value calculation framework to accurately quantify the criteria weights and reflect the criteria dependence. Finally, the Shapley value, gain and loss functions are extended to TODIM to construct the dominance, thus integrating the <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-SZFN-TODIM model. The <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40815_2025_2097_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upalpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">α</mi> </math></EquationSource> </InlineEquation>-SZFN-TODIM model can help enterprises to select the GPCDS with maximum benefits according to the risk preferences of decision makers. The model is applied to the evaluation of the new energy vehicles conceptual design schemes to verify the feasibility of the model. Subsequently, the sensitivity is verified by the change of the attenuation factor of the TODIM and the fluctuations of the criteria weights, and the robustness and feasibility of the model are verified by comparing with a variety of classical decision models. The final results show that the model is robust, efficient and reasonable for solving GPCDSs evaluation problem.</p>

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A multi-criteria decision model for evaluating green product conceptual design schemes based on \(\upalpha \)-spherical Z-fuzzy numbers and TODIM

  • Xiuli Geng,
  • Peng Zeng

摘要

With growing resource shortages and environmental concerns, countries are advancing green manufacturing and green product development. Evaluating green product conceptual design schemes (GPCDSs) is critical for green product innovation, this paper aims to establish a scientific evaluation model for GPCDSs. Firstly, the \(\upalpha \) α -sphere Z-fuzzy numbers ( \(\upalpha \) α -SZFNs) are defined to describe the evaluation information. It is a combination of spherical Z-fuzzy numbers (SZFNs) and \(\upalpha \) α -cuts, which retains the advantages of SZFNs in dealing with fuzziness and providing reliability constraints. Meanwhile, \(\upalpha \) α -cuts simplify the calculation process of SZFNs and reduce information loss. Then, an advantage degree formula is constructed for comparing \(\upalpha \) α -SZFNs to define gain and loss functions. Secondly, the \(\lambda \) λ -fuzzy measure, which is a non-additive measure with simple calculation process, is introduced into the Shapley value calculation framework to accurately quantify the criteria weights and reflect the criteria dependence. Finally, the Shapley value, gain and loss functions are extended to TODIM to construct the dominance, thus integrating the \(\upalpha \) α -SZFN-TODIM model. The \(\upalpha \) α -SZFN-TODIM model can help enterprises to select the GPCDS with maximum benefits according to the risk preferences of decision makers. The model is applied to the evaluation of the new energy vehicles conceptual design schemes to verify the feasibility of the model. Subsequently, the sensitivity is verified by the change of the attenuation factor of the TODIM and the fluctuations of the criteria weights, and the robustness and feasibility of the model are verified by comparing with a variety of classical decision models. The final results show that the model is robust, efficient and reasonable for solving GPCDSs evaluation problem.