On Some Construction Method and Orness Measure of Bi-Capacities

Bi-Choquet Integrals based on bi-capacities are very powerful aggregation operators introduced by Grabisch and Labreuche, and they can generalize Choquet Integrals. Bi-capacities can model a lager range of preferences than capacities. However, there are few existent knowledge about constructing bi-capacities, and there lacks the practical and reasonable orness/andness definitions for bi-capacities to present an effective optimism/pessimism indicator. We present a convenient way to generate bi-capacities. As the main proposal of this study, we propose an orness/andness definition for bi-capacities. Although structurally complex in defining, with the help of one interesting proposition related to bi-Choquet Integral, its reasonability in the way of constructing further proves it can indeed serve as a perfect generalization of orness/andness for capacities.