Group decision making using distances between unbalanced linguistic assessments

Abstract

Currently, societal and technological trends make decision-making environments more and more complex. Linguistic variables are used to enrich the assessment of decision makers. This fact leads to the computational techniques of unbalanced linguistic terms for group decision making in the literature. First, we redefine the concept of unbalanced linguistic term set. We use three vertices in a graph based on a uniformly distributed term set to represent the left, central, and right parts of an unbalanced linguistic term set. Our definition makes unbalanced linguistic terms more arbitrary compared with previous definitions. We combine the 2-tuple linguistic model to construct an approximation representation model, which pursues computational convenience and concision at the expense of accuracy. Second, we propose a distance measure between two vertices on the graph and prove its reasonability. We extend this measure to aggregate preference of unbalanced linguistic terms provided by decision makers. Finally, a numerical example is given to illustrate the feasibility and validity of the proposed model. Our methodology allows a decision maker to use diversified assessment spaces to construct his/her preference. Furthermore, by using the aggregated geodesic distance to measure the ranking of alternatives, the slight difference in assessments can be noticed and reflected in the ranking.