Some notes on the coincidence of the Choquet integral and the pan-integral

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00600441" target="_blank" >RIV/67985556:_____/25:00600441 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011424003245?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011424003245?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2024.109178" target="_blank" >10.1016/j.fss.2024.109178</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Some notes on the coincidence of the Choquet integral and the pan-integral

Popis výsledku v původním jazyce

In this note, we provide an example to show the weak (M)-property is really weaker than the (M)-property for some finite monotone measure defined on infinite space, and hence answer an open problem which was proposed in the paper (Li et al. (2023) [9]). We prove that if a monotone measure μ is autocontinuous, then the weak (M)-property and the (M)-property of μ are equivalent. We propose the concept of (C-P)-property of monotone measures and show a set of sufficient and necessary conditions that the Choquet integral coincides with the pan-integral. We further study the relationships between the Choquet integral and the pan-integral in the setting of the ordered pairs of monotone measures, and obtain some interesting properties.

Název v anglickém jazyce

Some notes on the coincidence of the Choquet integral and the pan-integral

Popis výsledku anglicky

In this note, we provide an example to show the weak (M)-property is really weaker than the (M)-property for some finite monotone measure defined on infinite space, and hence answer an open problem which was proposed in the paper (Li et al. (2023) [9]). We prove that if a monotone measure μ is autocontinuous, then the weak (M)-property and the (M)-property of μ are equivalent. We propose the concept of (C-P)-property of monotone measures and show a set of sufficient and necessary conditions that the Choquet integral coincides with the pan-integral. We further study the relationships between the Choquet integral and the pan-integral in the setting of the ordered pairs of monotone measures, and obtain some interesting properties.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

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

1872-6801

Svazek periodika

499

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

109178

Kód UT WoS článku

001354223900001

EID výsledku v databázi Scopus

2-s2.0-85208193348