The 2-additive decomposition integrals and their applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F25%3AA2603BS7" target="_blank" >RIV/61988987:17610/25:A2603BS7 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011425000557" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011425000557</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2025.109316" target="_blank" >10.1016/j.fss.2025.109316</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The 2-additive decomposition integrals and their applications

Popis výsledku v původním jazyce

Decomposition integral with respect to a capacity (monotone measure) is a common framework for unifying some nonlinear integrals, such as the Choquet, the Shilkret, the PAN, the PC, and the concave integrals. The formula of decomposition integral concerning capacities depends on the distinguished decomposition system under some constraints on the sets being considered for each related integral. The Möbius representation of a monotone set function is a fundamental concept permitting the derivation of simple expressions of nonlinear integrals. In this paper, we propose Möbius representation of some decomposition integrals based on Lovász idea of an extension of pseudo-boolean functions for the decomposition systems to get different types of decomposition integrals. Then, we introduce a new type of integral to unify the Choquet, Shilkret, PAN, and PC integrals in terms of the Möbius transform. Consequently, we then propose the expressions of computing decomposition integrals concerning a 2-additive capacity. Finally, an illustrative example is used to demonstrate the applicability of the proposed results and simplicity of computing the 2-additive decomposition integrals.

Název v anglickém jazyce

The 2-additive decomposition integrals and their applications

Popis výsledku anglicky

Decomposition integral with respect to a capacity (monotone measure) is a common framework for unifying some nonlinear integrals, such as the Choquet, the Shilkret, the PAN, the PC, and the concave integrals. The formula of decomposition integral concerning capacities depends on the distinguished decomposition system under some constraints on the sets being considered for each related integral. The Möbius representation of a monotone set function is a fundamental concept permitting the derivation of simple expressions of nonlinear integrals. In this paper, we propose Möbius representation of some decomposition integrals based on Lovász idea of an extension of pseudo-boolean functions for the decomposition systems to get different types of decomposition integrals. Then, we introduce a new type of integral to unify the Choquet, Shilkret, PAN, and PC integrals in terms of the Möbius transform. Consequently, we then propose the expressions of computing decomposition integrals concerning a 2-additive capacity. Finally, an illustrative example is used to demonstrate the applicability of the proposed results and simplicity of computing the 2-additive decomposition integrals.

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

—

Číslo periodika v rámci svazku

May 2025

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

—

Kód UT WoS článku

001428714300001

EID výsledku v databázi Scopus

2-s2.0-85217806296