Generalized C F1 F2 -integrals: from Choquet-like aggregation to ordered directionally monotone functions
This paper introduces the theoretical framework for a generalization of CF1F2 -integrals, a family of Choquet-like integrals used successfully in the aggregation process of the fuzzy reasoning mechanisms of fuzzy rule based classification systems. The proposed generalization, called by gCF1F2 -integ...
| Autores: | , , , , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/56160 |
| Acesso em linha: | https://hdl.handle.net/2454/56160 |
| Access Level: | acceso abierto |
| Palavra-chave: | Aggregation functions Pre-aggregation functions Choquet integral CF1F2 -integral Ordered directionally monotonicity Pseudo pre-aggregation function pair |
| Resumo: | This paper introduces the theoretical framework for a generalization of CF1F2 -integrals, a family of Choquet-like integrals used successfully in the aggregation process of the fuzzy reasoning mechanisms of fuzzy rule based classification systems. The proposed generalization, called by gCF1F2 -integrals, is based on the so-called pseudo pre-aggregation function pairs (F1,F2), which are pairs of fusion functions satisfying a minimal set of requirements in order to guarantee that the gCF1F2 -integrals to be either an aggregation function or just an ordered directionally increasing function satisfying the appropriate boundary conditions. We propose a dimension reduction of the input space, in order to deal with repeated elements in the input, avoiding ambiguities in the definition of gCF1F2 -integrals. We study several properties of gCF1F2 -integrals, considering different constraints for the functions F1 and F2, and state under which conditions gCF1F2 -integrals present or not averaging behaviors. Several examples of gCF1F2 -integrals are presented, considering different pseudo pre-aggregation function pairs, defined on, e.g., t-norms, overlap functions, copulas that are neither t-norms nor overlap functions and other functions that are not even pre-aggregation functions. |
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