On the equivalence of the Choquet, pan- and concave integrals on finite spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00477091" target="_blank" >RIV/67985556:_____/17:00477091 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.06.086" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.06.086</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.06.086" target="_blank" >10.1016/j.jmaa.2017.06.086</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the equivalence of the Choquet, pan- and concave integrals on finite spaces

Popis výsledku v původním jazyce

In this paper we introduce the concept of maximal cluster of minimal atoms on monotone measure spaces and by means of this new concept we continue to investigate the relation between the Choquet integral and the pan-integral on finite spaces. It is proved that the (M)-property of a monotone measure is a sufficient condition that the Choquet integral coincides with the pan-integral based on the usual addition + and multiplication. Thus, combining our recent results, we provide a necessary and sufficient condition that the Choquet integral is equivalent to the pan-integral on finite spaces. Meanwhile, we also use the characteristics of minimal atoms of monotone measure to present another necessary and sufficient condition that these two kinds of integrals are equivalent on finite spaces. The relationships among the Choquet integral, the pan-integral and the concave integral are summarized.

Název v anglickém jazyce

On the equivalence of the Choquet, pan- and concave integrals on finite spaces

Popis výsledku anglicky

In this paper we introduce the concept of maximal cluster of minimal atoms on monotone measure spaces and by means of this new concept we continue to investigate the relation between the Choquet integral and the pan-integral on finite spaces. It is proved that the (M)-property of a monotone measure is a sufficient condition that the Choquet integral coincides with the pan-integral based on the usual addition + and multiplication. Thus, combining our recent results, we provide a necessary and sufficient condition that the Choquet integral is equivalent to the pan-integral on finite spaces. Meanwhile, we also use the characteristics of minimal atoms of monotone measure to present another necessary and sufficient condition that these two kinds of integrals are equivalent on finite spaces. The relationships among the Choquet integral, the pan-integral and the concave integral are summarized.

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

2017

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

456

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

151-162

Kód UT WoS článku

000407667900008

EID výsledku v databázi Scopus

2-s2.0-85023597858