Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00531646" target="_blank" >RIV/67985556:_____/20:00531646 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.sciencedirect.com/science/article/pii/S0165011418305451" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418305451</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2019.01.009" target="_blank" >10.1016/j.fss.2019.01.009</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Generalized CF1F2-integrals: From Choquet-like aggregation to ordered directionally monotone functions
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Fuzzy Sets and Systems
ISSN
0165-0114
e-ISSN
—
Svazek periodika
378
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
NL - Nizozemsko
Počet stran výsledku
24
Strana od-do
44-67
Kód UT WoS článku
000495091300003
EID výsledku v databázi Scopus
2-s2.0-85061115962