0531646 20240103224328.820200818235959.9 85061115962 000495091300003 10.1016/j.fss.2019.01.009 24 s. P cav_un_epca*02566420165-01143781 (2020)44-67Elsevier Uninorm Fuzzy Implication Distributivity cav_un_auth*0330395 Dimuro G. P. BR 25 K cav_un_auth*0330393 Lucca G. ES 10 cav_un_auth*0298830 Bedregal B. BR 10 cav_un_auth*0101163 Mesiar Radko UTIA-B Ekonometrie Department of Econometrics E E Department of Econometrics 25 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0357025 Sanz A. ES 10 cav_un_auth*0394829 Ling S.-T. AU 10 cav_un_auth*0271524 Bustince H. ES 10 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. WOS BA 10000 10100 10102 2021 7 RVO:67985556 http://hdl.handle.net/11104/0310640 S 1* Article Computer Science Theory Methods|Mathematics Applied|Statistics Probability C COMPUTERSCIENCE.THEORY&METHODS|MATHEMATICS.APPLIED|STATISTICS&PROBABILITY 3.213 1.927 18.9 0.00736 0.706 17883 191 0.902 34.79 3.38 2053 Q1 2.960 218 Q1 48.968 85.8 Q3 Q2 1.86 Q1 93.396 2020 85061115962 SCOPUS PUBMED 000495091300003 WOS cav_un_epca*0256642 Fuzzy Sets and Systems 0165-0114 1872-6801 Roč. 378 č. 1 2020 44 67 Elsevier