A Picture Fuzzy Multiple Criteria Decision-Making Approach Based on the Combined TODIM-VIKOR and Entropy Weighted Method

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.