Paper Info
Title
Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions
Abstract
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.
Year
DOI
Venue
2020
10.1016/j.fss.2019.01.009
Fuzzy Sets and Systems
Keywords
Field
DocType
Aggregation functions,Pre-aggregation functions,Choquet integral,CF1F2-integral,Ordered directionally monotonicity,Pseudo pre-aggregation function pair
Discrete mathematics,Boundary value problem,Dimensionality reduction,Fuzzy reasoning,Copula (linguistics),Mathematics,Monotone polygon,Fuzzy rule
Journal
Volume
ISSN
Citations 
378
0165-0114
9
PageRank 
References 
Authors
0.46
0
7
Name
Order
Citations
PageRank
Graçaliz Pereira Dimuro166743.93
Giancarlo Lucca2734.60
Benjamín C. Bedregal375551.96
Radko Mesiar43778472.41
José Antonio Sanz542923.40
Chin-Teng Lin63840392.55
Humberto Bustince71938134.10