Sugeno integral and if ... then rules: the bipolar case

Sugeno integral is classically used in decision theory as an aggregation function to calculate a global evaluation for objects according to several criteria. Sugeno integral is relevant when evaluations are given on a qualitative totally ordered scale. Sugeno integral is equivalent to a system of thresholded if ... then rules. These selection or rejection rules are linked to the focal sets of the capacity or the conjugate of the capacity. When objects are evaluated on both positive and negative criteria, the evaluation scale is bipolar. In this case it is possible to aggregate local ratings using a bipolar extension of Sugeno integral. We show that this integral, called the CPTS integral, can also be interpreted in terms of if ... then rules.