A method based on shape-similarity for detecting similar opinions in group decision-making

In this paper, we propose a method to identify groups of similarly shaped membership functions representing criterion preferences provided by a large group of experts in the context of group decision-making. Our hypothesis hereby is that similarly shaped membership functions reflect similar expert opinions. The proposed method uses a symbolic notation to depict each membership function taking into account its shape characteristics (i.e., slopes and preference levels) and the relative length approximations on its X-axis segments (i.e., core segments, left and right spreads). The symbolic notation significantly reduces the complexity to handle a large group of expert opinions expressed by membership functions, and facilitates their comparison for grouping purposes through a shape-similarity measure. The main goal of the method is to detect all membership functions that are relevant to represent trends or suitable concepts among a large group of people considered as experts. An illustrative example, demonstrating the applicability of the method, is included in the paper.