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.

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.

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Nowadays, supply chain management (SCM) has achieved considerable attention from all over the world. q‐rung orthopair fuzzy set, developed by Yager, is the entirety of the most prominent tool to express fuzzy data in the decision‐making problems. In this study, the introduction of two new generalised measures (entropy and Jensen–Tsalli divergence measure) of q‐rung orthopair fuzzy information involving one real parameter is given. The proposed measures have satisfied all the necessary mathematical properties of being a measure. Then the introduced entropy and divergence measure is used to obtain the objective weights. Based on the proposed entropy and divergence measure, we proposed a new decision method to deal with multiple‐attribute group decision‐making problems under the q‐rung orthopair fuzzy environment. Then, on the basis of the TODIM and VIKOR techniques, an integrated TODIM‐VIKOR approach is developed to solve multiattribute group decision‐making problem. In this paper, TODIM aims to determine the overall dominance degree and VIKOR aims to determine the compromise solution. Lastly, we handle a supplier selection problem to verify the performance of the proposed q‐rung orthopair fuzzy TODIM‐VIKOR method and results explore the reliability and effectiveness of our proposed methodology by comparing the ranking solution with the ranking results of the existing approaches.