Performance impact of using $$C_T$$-integrals in the fuzzy reasoning method of a classification system

Abstract There are several ways to address classification problems. Frequently, these approaches rely on the issue of interpretative models. This point is closely related to the field of Explainable Artificial Intelligence. One commonly used approach for dealing with classification problems, producing accurate results with an understandable model, is Fuzzy Rule-Based Classification Systems. At the core of this method resides the Fuzzy Reasoning Methods, which use the knowledge base to derive conclusions from a pattern and a set of fuzzy (if-then) rules. This procedure is known to improve the generalization capability of classification systems. Moreover, the literature shows that applying the Choquet integral as an aggregation operator boosts the system quality. It also paved the way for creating different generalizations of this operator, like $$C_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:math> -integrals, which are generalizations by triangular norms (T-norms) with averaging characteristics. To the best of our knowledge, the Hamacher product excels on the $$C_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:math> -integrals, only being inferior to any generalization with non-averaging characteristics. This paper presents new generalizations by well-known parametric t-norms, demonstrating that some may be an alternative to the current state-of-the-art of the averaging functions’ universe. Graphic abstract