On the topological entropy on the space of fuzzy numbers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F14%3AA150103O" target="_blank" >RIV/61988987:17610/14:A150103O - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
čeština
Original language name
On the topological entropy on the space of fuzzy numbers
Original language description
In the main result of this article, we prove that the topological entropies of a given interval map and its Zadeh's extension (fuzzification) to the space of fuzzy numbers (i.e., the space of fuzzy sets with connected alpha-cuts) are the same. This result is in contrast with our previous result, which claimed that the topological entropy of the Zadeh's extension significantly increases for a majority of simple interval maps. In addition, we prove some properties of the limit sets of trajectories that are generated by iterating the fuzzy set valued function on connected fuzzy sets; for instance, we specify the shapes of the possible limit sets. Furthermore, the presented topics are studied for set-valued (induced) discrete dynamical systems. The main results are proved with a variational principle that describes the relations between topological entropy and measure-theoretical entropy.
Czech name
On the topological entropy on the space of fuzzy numbers
Czech description
In the main result of this article, we prove that the topological entropies of a given interval map and its Zadeh's extension (fuzzification) to the space of fuzzy numbers (i.e., the space of fuzzy sets with connected alpha-cuts) are the same. This result is in contrast with our previous result, which claimed that the topological entropy of the Zadeh's extension significantly increases for a majority of simple interval maps. In addition, we prove some properties of the limit sets of trajectories that are generated by iterating the fuzzy set valued function on connected fuzzy sets; for instance, we specify the shapes of the possible limit sets. Furthermore, the presented topics are studied for set-valued (induced) discrete dynamical systems. The main results are proved with a variational principle that describes the relations between topological entropy and measure-theoretical entropy.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SET SYST
ISSN
0165-0114
e-ISSN
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Volume of the periodical
257
Issue of the periodical within the volume
16.12.2014
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
14
Pages from-to
132-145
UT code for WoS article
000344424600008
EID of the result in the Scopus database
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