CC-integrals: Choquet-like Copula-based aggregation functions and its application in fuzzy rule-based classification systems

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• 作者：Giancarlo Lucca^a ; ^d ; ^{lucca.112793@e.unavarra.es} ; José ; Antonio Sanz^a ; ^c ; ^{joseantonio.sanz@unavarra.es} ; Graç ; aliz Pereira Dimuro ; ^a ; ^d ; ^{gracalizdimuro@furg.br} ; ^{gracaliz@gmail.com} ; Benjamí ; n Bedregal^e ; ^{bedregal@dimap.ufrn.br} ; Maria José ; Asiain^b ; ^{asiain@unavarra.es} ; Mikel Elkano^a ; ^c ; ^{elkano.mikel@gmail.com} ; Humberto Bustince^a ; ^c ; ^{bustince@unavarra.es}
• 关键词：Aggregation functions ; Choquet integral ; Copula ; t-norm ; Overlap function ; Fuzzy rule-based classification systems ; Fuzzy reasoning method
• 刊名：Knowledge-Based Systems
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：119
• 期：Complete
• 页码：32-43
• 全文大小：622 K
• 卷排序：119

文摘

This paper introduces the concept of Choquet-like Copula-based aggregation function (CC-integral) and its application in fuzzy rule-based classification systems. The standard Choquet integral is expanded by distributing the product operation. Then, the product operation is generalized by a copula. Unlike the generalization of the Choquet integral by t-norms using its standard form (i.e., without distributing the product operator), which results in a pre-aggregation function, the CC-integral satisfies all the conditions required for an aggregation function. We build some examples of CC-integrals considering different examples of copulas, including t-norms, overlap functions and copulas that are neither t-norms nor overlap functions. We show that the CC-integral based on the minimum t-norm, when applied in fuzzy rule-based classification systems, obtains a performance that is, with a high level of confidence, better than that which adopts the winning rule (maximum). We concluded that the behavior of CC-integral is similar to the best Choquet-like pre-aggregation function. Consequently, the CC-integrals introduced in this paper can enlarge the scope of the applications by offering new possibilities for defining fuzzy reasoning methods with a similar gain in performance.