The picture fuzzy set (PFS) has grown huge attention in the research area of uncertain information from the last few years. Information measures have been widely studied in various fuzzy environments. Therefore, in this paper, we study the entropy and divergence measures under the picture fuzzy environment. First, the paper introduced a new entropy measure to measure the fuzziness degree associated with a PFS. An example is established to show the capabilities of the proposed entropy measure. Second, the paper defines a new Jensen–Tsalli divergence measure for PFS to evaluate the information of discrimination between two PFS. We also discuss several properties of entropy and divergence measures in detail. Then we present a new method, based on proposed entropy and divergence measure, to determine the objective weights of experts for multicriteria group decision making with picture fuzzy information. The final criteria weights are obtained by combining subjective and objective weights for more reliable weightage of evaluation criteria. By using this comprehensive weight‐determination technique, the proposed method can effectively reduce the unreasonable impact of the extreme evaluation data on the evaluation results. Further, a new multi‐criteria decision‐making approach is developed based on the combining concepts of the TODIM and VIKOR method under the picture fuzzy environment. We used TODIM to obtain the overall dominance degree which considers the bounded rationality of decision makers and VIKOR is used to obtain the compromise ranking of alternatives. Lastly, an application of the proposed integrated model is demonstrated to verify the feasibility and usefulness and the outcomes of the proposed model are compared with the outcomes of the existing approaches to indicate its validity. This integrated method can effectively reduce the distortion of decision information and provide extraordinary evaluation results. The proposed approach is used in detecting the major issues due to which a company is facing such breakdowns.

中文翻译：

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一种基于熵和 Jensen-Tsalli 散度测度的新型 TODIM-VIKOR 方法，用于决策问题中的图片模糊集

近年来，图像模糊集（PFS）在不确定信息的研究领域引起了极大的关注。信息度量已在各种模糊环境中得到广泛研究。因此，在本文中，我们研究了图片模糊环境下的熵和发散度量。首先，论文引入了一种新的熵度量来衡量与 PFS 相关的模糊度。建立了一个例子来展示所提出的熵测度的能力。其次，本文为 PFS 定义了一种新的 Jensen-Tsalli 散度度量，以评估两个 PFS 之间的区分信息。我们还详细讨论了熵和散度测度的几个属性。然后我们提出了一种基于提出的熵和散度度量的新方法，利用图片模糊信息确定多准则群决策专家的客观权重。最终的标准权重是通过结合主观和客观权重获得的，以获得更可靠的评估标准权重。通过使用这种综合权重确定技术，所提出的方法可以有效减少极端评价数据对评价结果的不合理影响。此外，在图像模糊环境下，基于TODIM和VIKOR方法的结合概念，开发了一种新的多准则决策方法。我们使用TODIM获得考虑决策者有限理性的整体支配度，并使用VIKOR获得替代方案的折衷排名。最后，展示了拟议综合模型的应用，以验证可行性和有用性，并将拟议模型的结果与现有方法的结果进行比较，以表明其有效性。这种综合方法可以有效减少决策信息的失真，提供非凡的评价结果​​。建议的方法用于检测公司面临此类故障的主要问题。