Polynomial alias higher degree fuzzy transform of complex-valued functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F18%3A10236821" target="_blank" >RIV/61989100:27510/18:10236821 - isvavai.cz</a>
Alternative codes found
RIV/61988987:17610/18:A1901GGE
Result on the web
<a href="http://dx.doi.org/10.1016/j.fss.2017.06.011" target="_blank" >http://dx.doi.org/10.1016/j.fss.2017.06.011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2017.06.011" target="_blank" >10.1016/j.fss.2017.06.011</a>
Alternative languages
Result language
angličtina
Original language name
Polynomial alias higher degree fuzzy transform of complex-valued functions
Original language description
In this article, we propose a general approach to the computation of components of the direct higher degree fuzzy transform. Apart from the orthogonal bases of the subspaces of polynomials of weighted Hilbert spaces with respect to a generalized uniform fuzzy partition, which are used in all papers on fuzzy transform of higher degree, we admit also the non-orthogonal bases. An advantage of using non-orthogonal bases consists in the possibility of replacing orthogonal polynomials, derivation of which by the Gram-Schmidt orthogonalization process can be questionable difficult or imprecise, by suitable non-orthogonal polynomials of much simpler form. We present a simple matrix calculus and show how it can be used to introduce the components of the direct higher degree fuzzy transform. With the help of the monomial basis, we prove a convergence theorem and an approximation theorem for the higher degree fuzzy transform. The results are illustrated by examples including a comparison with standard methods.
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
50206 - Finance
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
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
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Volume of the periodical
342
Issue of the periodical within the volume
July
Country of publishing house
US - UNITED STATES
Number of pages
31
Pages from-to
1-31
UT code for WoS article
000432350400001
EID of the result in the Scopus database
2-s2.0-85023622557