Generalized C<inf>F<inf>1</inf>F<inf>2</inf></inf>-integrals: From Choquet-like aggregation to ordered directionally monotone functions

© 2019 Elsevier B.V. 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

Detection and monitoring of lung inflammation in cystic fibrosis during respiratory tract exacerbation using diffusion-weighted magnetic resonance imaging

The aim was to investigate whether diffusion-weighted magnetic resonance imaging (DWI) detects and monitors inflammatory and lung function changes during respiratory tract exacerbations (RTE) treatment in patients with cystic fibrosis (CF).29 patients with RTE underwent DWI pre- and post-antibiotic treatment. A control group of 27 stable patients, matched for age and sex, underwent DWI with the same time gap as those undergoing RTE treatment. Clinical status and lung function were assessed at each DWI time point. The CF-MRI scoring system was used to assess structural lung changes in both CF groups.Significant reduction in the DWI score over the course of antibiotic treatment (p&lt;0.0001) was observed in patients with RTE, but not in the control group. DWI score had a strong inverse correlation with clinical status (r=-0.504, p&lt;0.0001) and lung function (r=-0.635, p&lt;0.0001) in patients with RTE. Interestingly, there were persistent significant differences in the CF-MRI score between the RTE and control group at both baseline and follow-up (p&lt;0.001), while the differences in DWI score were only observed at baseline (p&lt;0.001).DWI is a promising imaging method for noninvasive detection of pulmonary inflammation during RTE, and may be used to monitor treatment efficacy of anti-inflammatory treatment