A New Picture Fuzzy Entropy and Its Application Based on Combined Picture Fuzzy Methodology with Partial Weight Information

Abstract

Picture fuzzy set (PFS) is more comprehensive tool than intuitionistic fuzzy set (IFS) for modeling the uncertain decision-making problems. In this paper, a new picture fuzzy entropy measure is proposed and proved that the proposed measure satisfies the axiomatic definition of entropy measures for picture fuzzy sets. Besides this, the useful mathematical properties of the new entropy measure are also investigated. The justification of the proposed picture fuzzy measure is established by discussing its particular cases and compares it with the existing entropy measures. Then, for the case where criteria weights are partially known, we used an entropy-based method to produce objective weights. For the uncertain environment, TODIM (portuguese acronym for interactive multicriteria decision-making) and ELECTRE methods are useful for practical problems. Based on the advantages of PFSs,TODIM, and ELECTRE, we proposed an integrated picture fuzzy TODIM-ELECTRE to combine the prominent benefits of these theories. We present the TODIM-ELECTRE model for PFS environment and express the computing steps in brief of this new established model. Thereafter, the superiority of the new model is verified by a numerical example of supplier selection and through comparative study with other existing methods.