On the topological entropy on the space of fuzzy numbers

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

čeština

Název v původním jazyce

On the topological entropy on the space of fuzzy numbers

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the topological entropy on the space of fuzzy numbers

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

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Svazek periodika

257

Číslo periodika v rámci svazku

16.12.2014

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

132-145

Kód UT WoS článku

000344424600008

EID výsledku v databázi Scopus

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