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

Kód výsledku v IS VaVaI

RIV/67985556:_____/20:00531646 - isvavai.cz

Výsledek na webu

https://www.sciencedirect.com/science/article/pii/S0165011418305451

DOI - Digital Object Identifier

10.1016/j.fss.2019.01.009

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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