In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.

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A key component of Fuzzy Rule-Based Classification Systems (FRBCSs) is the Fuzzy Reasoning Method (FRM), since it infers the class predicted for new examples. A crucial stage in any FRM is the way in which the information given by the fired rules during the inference process is aggregated. A widely used FRM is the winning rule, which applies the maximum to accomplish this aggregation. The maximum is an averaging operator, which means that its result is within the range delimited by the minimum and the maximum of the aggregated values. Over the last years, new averaging operators based on generalizations of the Choquet integral were also proposed to perform this aggregation process. However, the most accurate FRBCSs use the FRM known as additive combination, that considers the normalized sum as the aggregation operator, which is non-averaging. For this reason, this paper is aimed at introducing a new non averaging operator named CF 1 F 2integral, which is a generalization of the Choquet-like Copulabased integral (CC-integral). CF 1 F 2-integrals present the desired properties of an aggregation-like operator, since they satisfy appropriate boundary conditions and have some kind of increasingness property. We show that CF 1 F 2-integrals, when used to cope with classification problems, enhance the results of the previous averaging generalizations of the Choquet integral and they provide competitive results (even better) when compared with state-of-the-art FRBCSs. Index Terms-Fuzzy rule-based classification systems, Choquet Integral, CF 1 F 2-integrals, CC-integrals, OD monotone functions.

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