Application of GRA Method in Multi-Attribute Decision Making Problem Base on Picture Fuzzy Choquet Integral Information

Abstract

Picture fuzzy set (PFS) is the generalize structure over existing structures of fuzzy sets to arrange uncertainty and imprecise information in the decision making problem. Picture fuzzy set is a direct extension of the intuitionistic fuzzy set (IFS) that can model uncertainty in situations with multiple types of answers, such as yes, no, abstain, and refuse. In this paper, we propose Choquet integral (CI) for the picture fuzzy set (PFS). Then, we defined some basic operational laws for picture fuzzy set. Also, based on the defined operational laws, we proposed picture fuzzy averaging (PFA) and picture fuzzy Choquet integral weighted averaging operator (PFCIWAO) along with their basic properties. Also, we propose the normalized Hamming distance and normalized Euclidean distance for the picture fuzzy numbers. Viewing the electiveness of the picture fuzzy set, we proposed a decision-making approach for the multi-criteria decision-making problems. We also propose the GRA method using Choquet integral for dealing uncertainty in decision making problems under picture fuzzy information. Lastly, we illustrate an example show the effectiveness and reliability of the proposed method.