A Proposal for Tuning the Alpha Parameter in a Copula Function Applied in Fuzzy Rule-Based Classification Systems

In this paper, we use the concept of extended Choquet integral generalized by a copula function, as proposed by Lucca et al. More precisely, the copula considered in their study uses a variable alpha , with different fixed values for testing its behavior. In this contribution we propose a modification of this method assigning a value to this alpha parameter using a genetic algorithm in order to find the value that best fits it for each class. Specifically, this new proposal is applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCSs). Finally, we compare the results provided by our new approach against the best solution proposed by Lucca et al. (that uses an fixed value for the variable alpha ). From the obtained results it can be concluded that the genetic learning of the alpha parameter is statistically superior than the fixed one. Therefore, we demonstrate that our genetic method can be used as an alternative for this function.