Picture fuzzy Additive Ratio Assessment Method (ARAS) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for multi-attribute decision problem and their application

The purpose of this paper is to study the multi-attribute decision-making problem under the fuzzy picture environment. First, a method to compare the pros and cons of picture fuzzy numbers (PFNs) is introduced in this paper. Second, the correlation coefficient and standard deviation (CCSD) method is used to determine the attribute weight information under the picture fuzzy environment regardless of whether the attribute weight information is partially unknown or completely unknown. Third, the ARAS and VIKOR methods are extended to the picture fuzzy environment, and the proposed PFNs comparison rules are also applied in the PFS-ARAS and PFS-VIKOR methods. Fourth, the problem of green supplier selection in a picture-ambiguous environment is solved by the method proposed in this paper. Finally, the method proposed in this paper is compared with some methods and the results are analyzed.