Picture fuzzy set theory developed by Cuong and Kreinovich is an extension of the fuzzy set theory and intuitionistic fuzzy set theory. In this paper, we proposed a new framework for picture fuzzy entropy from a probabilistic viewpoint. The justification of the proposed axiomatic structure is established by offering a new information measure based on Shannon entropy under picture fuzzy environment and also studied its mathematical properties. Besides, we developed an algorithm for picture fuzzy set with the help of TODIM (a Portuguese acronym for Interactive Multi-Criteria Decision Making) and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) methods to explain the multi-criteria decision-making (MCDM) problems with picture fuzzy numbers. Finally, two numerical examples are given to verify the proposed approach based on opinion surveys to anticipate the election results and the output is reasonably compared with other MCDM method existing in the literature, what’s more, the viable experiment results are gotten.

Cuong和Kreinovich提出的图片模糊集理论是模糊集理论和直觉模糊集理论的延伸。本文从概率的角度提出了一种图片模糊熵的新框架。通过在图像模糊环境下提供基于香农熵的新信息量度，来建立所提出的公理结构的理由，并研究其数学性质。此外，我们借助TODIM（交互式多标准决策的葡萄牙语缩写）和VIKOR（VlseKriterijumska Optimizacija I Kompromisno Resenje）方法开发了一种图片模糊集算法，以解释多标准决策（MCDM）问题图片模糊数字。最后，