Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions

0531646 - ÚTIA 2021 RIV NL eng J - Článek v odborném periodiku
Dimuro, G. P. - Lucca, G. - Bedregal, B. - Mesiar, Radko - Sanz, A. - Ling, S.-T. - Bustince, H.
Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions.
Fuzzy Sets and Systems. Roč. 378, č. 1 (2020), s. 44-67. ISSN 0165-0114. E-ISSN 1872-6801
Institucionální podpora: RVO:67985556
Klíčová slova: Uninorm * Fuzzy Implication * Distributivity
Obor OECD: Applied mathematics
Impakt faktor: 3.343, rok: 2020
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2020/E/mesiar-0531646.pdf https://www.sciencedirect.com/science/article/pii/S0165011418305451

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.
Trvalý link: http://hdl.handle.net/11104/0310640