Sustainable supplier selection (SSS) is an important part of sustainable supply chain management (SSCM). In this paper, an integrated multi-criteria decision-making (MCDM) framework, based on the picture fuzzy exponential entropy, and the VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) method, is proposed to manage SSS problems. Firstly, the evaluation criteria of SSS, including economic, environmental and social, is established. This can be evaluated in the form of the actual data or linguistic terms provided by suppliers and experts respectively in an actual decision-making process. Then, according to the translated scales, all the evaluation information can be converted into picture fuzzy numbers (PFNs). Secondly, the picture fuzzy exponential entropy is defined. Moreover, based on the entropy’s minimization principle, the defined picture fuzzy exponential entropy is used to determine the weight of the SSS’s criteria. Thirdly, the extended VIKOR method, which combines the grey correlation coefficient, is utilized to select a suitable supplier. This method avoids the shortcomings of the traditional VIKOR method in data mining and solves the conflict between SSS criteria. Finally, the feasibility and effectiveness of the proposed integrated decision framework are verified by an experiment, as well as a sensitivity analysis and comparative analysis.

中文翻译：

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图像模糊环境下可持续供应商选择的综合多标准决策框架

可持续供应商选择（SSS）是可持续供应链管理（SSCM）的重要组成部分。在本文中，提出了一种基于图片模糊指数熵和 VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) 方法的集成多准则决策 (MCDM) 框架来管理 SSS 问题。首先，建立SSS的评价标准，包括经济、环境和社会。这可以通过供应商和专家在实际决策过程中分别提供的实际数据或语言术语的形式进行评估。然后，根据转换后的尺度，所有的评价信息都可以转换为图片模糊数（PFNs）。其次，定义了图片模糊指数熵。此外，基于熵的最小化原理，定义的图片模糊指数熵用于确定 SSS 标准的权重。第三，结合灰色相关系数的扩展VIKOR方法用于选择合适的供应商。该方法避免了传统VIKOR方法在数据挖掘方面的不足，解决了SSS准则之间的冲突。最后，通过实验、敏感性分析和对比分析验证了所提出的综合决策框架的可行性和有效性。该方法避免了传统VIKOR方法在数据挖掘方面的不足，解决了SSS准则之间的冲突。最后，通过实验、敏感性分析和对比分析验证了所提出的综合决策框架的可行性和有效性。该方法避免了传统VIKOR方法在数据挖掘方面的不足，解决了SSS准则之间的冲突。最后，通过实验、敏感性分析和对比分析验证了所提出的综合决策框架的可行性和有效性。