Sugeno Integrals and the Commutation Problem

Abstract

In decision problems involving two dimensions (like several agents and several criteria) the properties of expected utility ensure that the result of a multicriteria multiperson evaluation does not depend on the order with which the aggregations of local evaluations are performed (agents first, criteria next, or the converse). We say that the aggregations on each dimension commute. Ben Amor, Essghaier and Fargier have shown that this property holds when using pessimistic possibilistic integrals on each dimension, or optimistic ones, while it fails when using a pessimistic possibilistic integral on one dimension and an optimistic one on the other. This paper studies and completely solves this problem when Sugeno integrals are used in place of possibilistic integrals, indicating that there are capacities other than possibility and necessity measures that ensure commutation of Sugeno integrals.

Equilibrium under uncertainty with Sugeno payoff

“…So, the difference is only in terms. It is also shown in [25] that the notion of tensor product coincides with the method of aggregation of capacities considered in [7].…”

Commuting Double Sugeno Integrals

“…is not a necessity measure and µ X is not a possibility measure. Obeying the two inequalities (6) and 7enforces the following constraints in the Boolean case µ Y possibility measure or µ X necessity measure and µ Y necessity measure or µ X possibility measure.…”