Using consensus and distances between generalized multi-attribute linguistic assessments for group decision-making

This paper proposes a mathematical framework and methodology for group decision-making under multi-granular and multi-attribute linguistic assessments. It is based on distances between linguistic assessments and a degree of consensus. Distances in the space of qualitative assessments are defined from the geodesic distance in graph theory and the Minkowski distance. The degree of consensus is defined through the concept of entropy of a qualitatively-described system. Optimal assessments in terms of both proximity to all the expert opinions in the group and the degree of consensus are used to compare opinions and define a methodology to rank multi-attribute alternatives.