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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Volume of the periodical

378

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

24

Pages from-to

44-67

UT code for WoS article

000495091300003

EID of the result in the Scopus database

2-s2.0-85061115962