CF-integrals: A new family of pre-aggregation functions with application to fuzzy rule-based classification systems

This paper introduces the family of CF-integrals, which are pre-aggregations functions that generalizes the Choquet integral considering a bivariate function F that is left 0-absorbent. We show that CF-integrals are 1→-pre-aggregation functions, studying in which conditions they are idempotent and/or averaging functions. This characterization is an important issue of our approach, since we apply these functions in the Fuzzy Reasoning Method (FRM) of a fuzzy rule-based classification system and, in the literature, it is possible to observe that non-averaging aggregation functions usually provide better results. We carry out a study with several subfamilies of CF-integrals having averaging or non-averaging characteristics. As expected, the proposed non-averaging CF-integrals obtain more accurate results than the averaging ones, thus, offering new possibilities for aggregating accurately the information in the FRM. Furthermore, it allows us to enhance the results of classical FRMs like the winning rule and the additive combination.