Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem

Distance measurement is an important technique for determining the similarity of two Picture Fuzzy Sets (PFSs). The article presents a novel idea of distance measure for PFSs, which is then applied to solve Multi-Criteria Decision-Making (MCDM) problems. By using the distance measure of the PFSs, the TOPSIS approach is applied to solve MCDM problems. The score function is employed to determine the best alternatives for both Picture Fuzzy Positive Ideal Solution (PFPIS) and Picture Fuzzy Negative Ideal Solutions (PFNIS). The options are ranked using the revised index technique and the relative closeness coefficient method. An illustrative numerical example is provided to demonstrate the feasibility and practicality of the proposed distance measure for PFSs.