Picture fuzzy set (PFS) is more effective tool for handling the uncertainty and vagueness in the real world and it can contain more information than intuitionistic fuzzy set (IFS). In this paper, we proposed a new entropy measure in terms of PFSs and some of its properties are discussed in detail. An example involving linguistic variables is established to show the validity of the proposed information measure. Furthermore, we proposed an entropy-based decision-making method to solve picture fuzzy MCDM (multi-criteria decision-making) problems with the integration of subjective and objective weights to make the evaluation result more objectively. Besides, we used TODIM (a Portuguese acronym for Interactive Multi-Criteria Decision-Making) to obtain the overall dominance degrees and VIKOR (VlseKriterijumska Op-timizacija I Kompromisno Resenje) is used to obtain the compromise ranking of alternatives in the framework of PFS and so-called TODIM-VIKOR. An illustrative example is developed to demonstrate the validity and reliability of the proposed approach and compared the results with some existing approaches. The proposed TODIM-VIKOR approach is more suitable than the existing ones to deal with uncertain and imprecise information and offers numerous choices to the decision-maker for accessing the finest alternatives.

MS Classification: 94A15, 94A24, 26D15

图片模糊集（PFS）是处理现实世界中的不确定性和模糊性的更有效工具，它可以包含比直觉模糊集（IFS）更多的信息。在本文中，我们根据 PFS 提出了一种新的熵度量，并详细讨论了它的一些特性。建立了一个涉及语言变量的例子来表明所提出的信息度量的有效性。此外，我们提出了一种基于熵的决策方法来解决图片模糊MCDM（多标准决策）问题，结合主客观权重，使评估结果更加客观。除了，我们使用 TODIM（Interactive Multi-Criteria Decision-Making 的葡萄牙语首字母缩写词）来获得总体优势度，并使用 VIKOR (VlseKriterijumska Op-timizacija I Kompromisno Resenje) 来获得 PFS 框架中替代方案的折衷排名，因此 -称为 TODIM-VIKOR。开发了一个说明性示例来证明所提出方法的有效性和可靠性，并将结果与​​一些现有方法进行比较。提议的 TODIM-VIKOR 方法比现有方法更适合处理不确定和不精确的信息，并为决策者提供多种选择以获取最佳替代方案。开发了一个说明性示例来证明所提出方法的有效性和可靠性，并将结果与​​一些现有方法进行比较。提议的 TODIM-VIKOR 方法比现有方法更适合处理不确定和不精确的信息，并为决策者提供多种选择以获取最佳替代方案。开发了一个说明性示例来证明所提出方法的有效性和可靠性，并将结果与​​一些现有方法进行比较。提议的 TODIM-VIKOR 方法比现有方法更适合处理不确定和不精确的信息，并为决策者提供多种选择以获取最佳替代方案。

MS 分类：94A15、94A24、26D15