Mobius representation of the bipolar decomposition integrals and its applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633256" target="_blank" >RIV/61989592:15310/25:73633256 - isvavai.cz</a>
Result on the web
<a href="https://ijfs.usb.ac.ir/article_9334_29663ccc78330f6538eba9baff213e26.pdf" target="_blank" >https://ijfs.usb.ac.ir/article_9334_29663ccc78330f6538eba9baff213e26.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.22111/ijfs.2025.9334" target="_blank" >10.22111/ijfs.2025.9334</a>

Result language
angličtina
Original language name
Mobius representation of the bipolar decomposition integrals and its applications
Original language description
The bipolar decomposition integral, recently introduced in [5], is a general framework for handling integrals related to aggregation on unipolar and bipolar scales. The Möbius representation is related to the notion of k-additivity of a monotone set function and allows to derive simple expressions of some nonlinear integrals. In this paper, we propose Möbius representation for the bipolar decomposition integral, which includes the Möbius representation of each of the bipolar Choquet integral, bipolar Shilkret integral, and bipolar Pan integral. Then, we introduce the expressions for computing bipolar decomposition integrals concerning a 2-additive bi-capacity. Lastly, a practical numerical example is provided to illustrate the applicability of the proposed results in dealing with aggregation on bipolar scales, and simplicity of calculating the 2-additive bipolar decomposition integrals.
Czech name
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Czech description
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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
10102 - Applied mathematics

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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