Generalizing the GMC-RTOPSIS Method using CT-integral Pre-aggregation Functions

In Multi-Criteria Decision Making, one of the most used algorithm designed to deal with decision making is the Technical Order by Preference to Ideal Solution (TOPSIS), which is based on finding a solution that is close to the best possible solution and distant from the worst possible solution. The Group Modular Choquet Random TOPSIS (GMC-RTOPSIS) is a generalization of the TOPSIS method capable of dealing with multiple and heterogeneous data types and interaction among criteria by means of the discrete Choquet integral. On the other hand, CT-integrals are a generalization of the Choquet integral using t-norms, which are more flexible than the standard Choquet integral. CT-integrals are pre-aggregation functions, which means that we do not require them to be monotonic in the whole domain, just in some specific directions, that is, they are directionally monotonic. Due to the excellent performance of CT-integrals in classification and multimodal fuzzy fusion decision problems, the objective of this paper is to generalize the GMC-RTOPSIS by using CT-integrals and to analyze the results provided by the use of five different t-norms in an example of a decision making problem.