CMin-Integral: A Choquet-Like Aggregation Function Based on the Minimum t-Norm for Applications to Fuzzy Rule-Based Classification Systems
This paper studies the concept of Choquet-like copula-based aggregation function (CC-integral), introduced by Lucca et al. , when one considers the Minimum t-norm, showing an application in fuzzy rule-based classification systems. The CC-integral is built from the standard Choquet integral, which is expanded by distributing the product operation, and, then, the product operation is generalized by a copula. In this paper, we study the behavior of this aggregation function in fuzzy rule-based classification systems, when one considers the Minimum t-norm as de copula of the CC-integral, which we call the CMin-integral. We show that the CMin-integral obtains a performance that is, with a high level of confidence, better than the approach that adopts the winning rule (maximum). Moreover, its behaviour is similar to the best Choquet-like pre-aggregation functions, introduced by Lucca et al. , with excellent performance. Consequently, the CMin-integral enlarge the scope of the applications by offering new possibilities for defining fuzzy reasoning methods with a similar gain in performance.
This work is supported by Brazilian National Counsel of Technological and Scientific Development CNPq (under the Processes 233950/2014-1, 305882/2016-3, 307781/2016-0) and by the Spanish Ministry of Science and Technology (under project TIN2016-77356-P). G.P. Dimuro is also supported by Caixa and Fundación Caja Navarra of Spain.
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