On the Completion Mechanism Produced by the Choquet Integral on Some Decision Strategies

Preference modeling consists in constructing a preference relation from initial preferences given by a decision maker. We are interested in the preference relation obtained from the use of the Choquet integral. The necessity preference is constructed as the intersection of all preference relations corresponding to a Choquet integral which are compatible with the initial preferences of the decision maker. We study some properties of this necessity relation on some classes of initial preferences. This gives some properties on the completion or extension ability of the Choquet integral. Keywords— Choquet integral, capacity, initial preferences.