Weighting Models to Generate Weights and Capacities in Multicriteria Group Decision Making

In multicriteria group decision-making problems, we need to determine the relative importances among criteria as well as among experts. When doing so, however, we often face the situations where consensuses within experts over different criteria need to be considered, and where uncertainties arise when experts do evaluations. Therefore, we need some special and reasonable methods to generate weights in such situations. In this study, three elaborately devised methods suggest ways to generate relative importance among experts, criteria, and the combination of them, respectively. The first one elicits the consensus extents within experts over different criteria, by which it can generate suitable weights among different criteria. The second one fully considers the uncertain nature when experts do evaluations, and proposes a fuzzy model which can generate weighting vector among experts according to the certainty degrees of valuations given by all the experts. In the last method, when relative importances among both experts and criteria are predetermined in the form of two capacities with dimension
n
and
m
, respectively, we find an interesting mechanism to successfully melt them into one
nm
-dimensional capacity which is based on given cognitive strength and on the proposed concept of compromised active/passive consensus.