Rule correlation and Choquet integration in fuzzy inference systems

We propose an extension of the Takagi-Sugeno-Kang (TSK) fuzzy inference system, using Choquet integration for aggregating the single rule outputs. In the new Choquet-TSK fuzzy inference system, the pairwise synergies between rules are encoded in a rule correlation matrix computed from the activation pattern of the rule base. The rule correlation matrix is then used to modulate the parameters of the Choquet integration scheme in order to compensate for the effect of rule synergies, which are present in most rule bases to a higher or lesser extent. The standard TSK fuzzy inference system remains a particular instance of the proposed Choquet-TSK extension and corresponds to the ideal case of rule independence. However, when rule correlation is present, the Choquet-TSK fuzzy inference system takes it into account when computing the final output of the system. On the basis of the rule correlation matrix, the new aggregation scheme of the Choquet-TSK fuzzy inference system attenuates the effective weight of positively correlated rules and emphasizes that of negatively correlated rules. Some case studies are discussed in order to illustrate the proposed methodology.