Data-Driven Modeling with Fuzzy Sets and Manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302DUN" target="_blank" >RIV/61988987:17610/22:A2302DUN - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0888613X22001001" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X22001001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijar.2022.07.009" target="_blank" >10.1016/j.ijar.2022.07.009</a>

Result language
angličtina
Original language name
Data-Driven Modeling with Fuzzy Sets and Manifolds
Original language description
The manifold hypothesis states that the shape of the observed data is relatively simple and that it lies on a low-dimensional manifold embedded in a high-dimensional space. We contribute to the problem of data-driven modeling by treating it as an inverse problem where the model defines a Euclidean space with a Riemannian manifold structure. In particular, our contribution shows that a fuzzy set on a bounded support defines a Riemannian manifold that can be embedded in a multidimensional space where dimension is a model parameter. A noticeable advantage of the proposed approach is its connection with the values of the membership function and independence from the dimension of the data being modeled. Last but not least, we have found various formal representations of the Laplace-Beltrami operator and use its values as an estimate of the quality of the approximate solution to the inverse problem.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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