A novel TODIM-VIKOR approach based on entropy and Jensen-Tsalli divergence measure for picture fuzzy sets in a decision-making problem

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. Therefore, in this paper, we study the entropy and divergence measures under the picture fuzzy environment. First, the paper introduced a new entropy measure to measure the fuzziness degree associated with a PFS. An example is established to show the capabilities of the proposed entropy measure. Second, the paper defines a new Jensen-Tsalli divergence measure for PFS to evaluate the information of discrimination between two PFS. We also discuss several properties of entropy and divergence measures in detail. Then we present a new method, based on proposed entropy and divergence measure, to determine the objective weights of experts for multicriteria group decision making with picture fuzzy information. The final criteria weights are obtained by combining subjective and objective weights for more reliable weightage of evaluation criteria. By using this comprehensive weight-determination technique, the proposed method can effectively reduce the unreasonable impact of the extreme evaluation data on the evaluation results. Further, a new multi-criteria decision-making approach is developed based on the combining concepts of the TODIM and VIKOR method under the picture fuzzy environment. We used TODIM to obtain the overall dominance degree which considers the bounded rationality of decision makers and VIKOR is used to obtain the compromise ranking of alternatives. Lastly, an application of the proposed integrated model is demonstrated to verify the feasibility and usefulness and the outcomes of the proposed model are compared with the outcomes of the existing approaches to indicate its validity. This integrated method can effectively reduce the distortion of decision information and provide extraordinary evaluation results. The proposed approach is used in detecting the major issues due to which a company is facing such breakdowns.