Number of the records: 1

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

SYSNO ASEP	0531646
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions
Author(s)	Dimuro, G. P. (BR) Lucca, G. (ES) Bedregal, B. (BR) Mesiar, Radko (UTIA-B)_{RID, ORCID} Sanz, A. (ES) Ling, S.-T. (AU) Bustince, H. (ES)
Number of authors	7
Source Title	Fuzzy Sets and Systems. - : Elsevier - ISSN 0165-0114 Roč. 378, č. 1 (2020), s. 44-67
Number of pages	24 s.
Publication form	Print - P
Language	eng - English
Country	NL - Netherlands
Keywords	Uninorm ; Fuzzy Implication ; Distributivity
Subject RIV	BA - General Mathematics
OECD category	Applied mathematics
Method of publishing	Limited access
Institutional support	UTIA-B - RVO:67985556
UT WOS	000495091300003
EID SCOPUS	85061115962
DOI	10.1016/j.fss.2019.01.009
Annotation	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.
Workplace	Institute of Information Theory and Automation
Contact	Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
Year of Publishing	2021
Electronic address	https://www.sciencedirect.com/science/article/pii/S0165011418305451

Number of the records: 1