Analyzing the behavior of aggregation and pre-aggregation functions in fuzzy rule-based classification systems with data complexity measures

Abstract

In our previous works, we have generalized the Choquet integral by replacing the product by t-norms and copula functions. This generalization has led to new theoretical results in the field of aggregations functions and it has allowed to define a new concept named pre-aggregation function. We applied this generalization in the fuzzy reasoning method of fuzzy rule-based classification systems with the aim of aggregating the information given by the fired rules so that global information associated with the classes of the problem can be derived. In these works, we have shown that this application is successful since it has allowed to enhance the behavior of a classical averaging aggregation operator like the maximum, which is used in the fuzzy reasoning method of the winning rule. In this contribution, we aim at studying whether there are characteristics of the datasets that allow one to know whether an aggregation function will work better then others or not.