The 2-additive decomposition integrals and their applications
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The 2-additive decomposition integrals and their applications
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fuzzy Sets and Systems
ISSN
0165-0114
e-ISSN
1872-6801
Volume of the periodical
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Issue of the periodical within the volume
May 2025
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
11
Pages from-to
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UT code for WoS article
001428714300001
EID of the result in the Scopus database
2-s2.0-85217806296