Dynamic programming algorithm-based picture fuzzy clustering approach and its application to the large-scale group decision-making problem

Due to the rapid development of society and economy, the large-scale group decision making (LSGDM) problems are increasingly common in the real life. In this paper, a dynamic programming algorithm-based picture fuzzy clustering approach is proposed to solve the LSGDM problems. First, aimed at the limitations of the existing operation laws of picture fuzzy sets, we define some new picture fuzzy operation laws. Based on these operation laws, a new picture fuzzy weighted geometric operator is developed to aggregate the preference information provided by the decision makers. Second, a new picture fuzzy Dice similarity measure is proposed to detect the different correlations between the decision makers. Then, inspired by the dynamic programming algorithm, a new clustering approach is proposed to improve the efficiency and quality of the decision-making. After the clustering process, the picture fuzzy score function is employed to compare and rank the alternatives. Finally, an illustrative example and a comparative analysis are provided to demonstrate the effectiveness and superiority of the proposed method.