A new picture fuzzy information measure based on shannon entropy with applications in opinion polls using extended VIKOR-TODIM approach

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.