Centralized ordered weighted averaging operator weights and their properties

We propose a method for generating ordered weighted averaging (OWA) operator weights based on a preference order expressed through a set of inequalities representing the relative importance of criteria. The resulting centralized OWA (COWA) operator weights are: (i) computationally derived by averaging the coordinates of the extreme points of the feasible set; (ii) mathematically defined as the weights that minimize the sum of squared deviations from each extreme point; (iii) geometrically located at the center of the feasible region defined by the inequalities.

Moreover, for several sets of inequalities, the COWA operator weights closely resemble those of the maximum entropy OWA operator and consistently exhibit a constant attitudinal character (AC), regardless of the number of criteria.

For validation purposes, we introduce a method for generating COWA operator weights that satisfy a specified AC, and demonstrate their similarity to the maximum entropy OWA operator weights through sample tests with varying number of criteria and AC values. The strength of the preference order associated with a specific AC provides deeper insight into how the AC relates to the ordinal relationships among the criteria.