The Cube of Opposition and the Complete Appraisal of Situations by Means of Sugeno Integrals

Abstract

The cube of opposition is a logical structure that underlies many information representation settings. When applied to multiple criteria decision, it displays various possible aggregation attitudes. Situations are usually assessed by combinations of properties they satisfy, but also by combinations of properties they do not satisfy. The cube of opposition applies to qualitative evaluation when criteria are weighted as well as in the general case where any subset of criteria may be weighted for expressing synergies between them, as for Sugeno integrals. Sugeno integrals are well-known as a powerful qualitative aggregation tool which takes into account positive synergies between properties. When there are negative synergies between properties we can use the so-called desintegral associated to the Sugeno integral. The paper investigates the use of the cube of opposition and of the if-then rules extracted from these integrals and desintegrals in order to better describe acceptable situations.