期刊
INFORMATION FUSION
卷 57, 期 -, 页码 27-43出版社
ELSEVIER
DOI: 10.1016/j.inffus.2019.10.005
关键词
Aggregation functions; Pre-aggregation functions; Pseudo pre-aggregation function pair; Ordered directionally monotonicity; Choquet integral; C-T-integral; C-F-integral; CC-integral; C-F1F2-Integral; gC(F1F2)-Integral
资金
- CNPq [233950/2014-1, 307781/2016-0]
- Spanish Ministry of Science and Technology [TIN2016-81731-REDT, TIN2016-77356-P]
- Government of Navarra [PC093-094 TFIPDL]
- Fundacion Caja Navarra
- Ministry of Education, Science, Research and Sport of the Slovak Republic (Research and Development Operational Programme for the project University Science Park of STU Bratislava) [ITMS 26240220084]
- European Regional Development Fund
- Czech Science Foundation (GACR) [18-06915S]
In 2013, Barrenechea et al. used the Choquet integral as an aggregation function in the fuzzy reasoning method (FRM) of fuzzy rule-based classification systems. After that, starting from 2016, new aggregation-like functions generalizing the Choquet integral have appeared in the literature, in particular in the works by Lucca et al. Those generalizations of the Choquet integral, namely C-T-integrals (by t-norm T), C-F-integrals(by a fusion function F satisfying some specific properties), CC-integrals (by a copula C), C-F1F2-integrals (by a pair of fusion functions (F-1, F-2) under some specific constraints) and their generalization gC(F)(1F2)-integrals, achieved excellent results in classification problems. The works by Lucca et al. showed that the aggregation task in a FRM may be performed by either aggregation, pre-aggregation or just ordered directional monotonic functions satisfying some boundary conditions, that is, it is not necessary to have an aggregation function to obtain competitive results in classification. The aim of this paper is to present and discuss such generalizations of the Choquet integral, offering a general panorama of the state of the art, showing the relations and intersections among such five classes of generalizations. First, we present them from a theoretical point of view. Then, we also summarize some applications found in the literature.
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