Using distances between unbalanced linguistic assessments for group decision-making

Abstract

In most decision making problems where linguistic assessments are used, the assessments are assumed to base on uniform and symmetrical distributed linguistic term set. However, there exist decision making problems whose assessments are unbalanced linguistic term sets. According to these problems, we propose a new linguistic representation model for group decision. Assuming that an unbalanced linguistic term is composed of left, central and right parts, we use three vertices in a graph based on uniform distributed term set to represent the unbalanced term. Then we define a distance measure between two unbalanced terms. We find a vertex in the graph which has the minimal distance with assessments. We use this vertex as the aggregated preference of different decision makers. Finally, a numerical example is illustrated in this paper. The new method enriches the assessment of decision makers and makes group decision making easier.