Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle
Let X denote a compact metric space and let f : X→X be a continuous map. It is known that a discrete dynamical system (X,f) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of X. In 2011, a new generalized form of Zadeh’s extensi...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/956467 |
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| author | Yaoyao Lan Chunlai Mu |
| author_facet | Yaoyao Lan Chunlai Mu |
| author_sort | Yaoyao Lan |
| collection | DOAJ |
| description | Let X denote a compact metric space and let f : X→X be a continuous map. It is known that a discrete dynamical system (X,f) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of X. In 2011, a new generalized form of Zadeh’s extension principle, so-called g-fuzzification, had been introduced by Kupka 2011. In this paper, we study the relations between Martelli’s chaotic properties of the original and g-fuzzified system. More specifically, we study the transitivity, sensitivity, and stability of the orbits in system (X,f) and its connections with the same ones in its g-fuzzified system. |
| format | Article |
| id | doaj-art-ab7ca7751f9c46758e820c5b09587d10 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ab7ca7751f9c46758e820c5b09587d102025-02-03T06:08:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/956467956467Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension PrincipleYaoyao Lan0Chunlai Mu1College of Computer Science, Chongqing University, Chongqing 401331, ChinaCollege of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaLet X denote a compact metric space and let f : X→X be a continuous map. It is known that a discrete dynamical system (X,f) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of X. In 2011, a new generalized form of Zadeh’s extension principle, so-called g-fuzzification, had been introduced by Kupka 2011. In this paper, we study the relations between Martelli’s chaotic properties of the original and g-fuzzified system. More specifically, we study the transitivity, sensitivity, and stability of the orbits in system (X,f) and its connections with the same ones in its g-fuzzified system.http://dx.doi.org/10.1155/2014/956467 |
| spellingShingle | Yaoyao Lan Chunlai Mu Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle Journal of Applied Mathematics |
| title | Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle |
| title_full | Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle |
| title_fullStr | Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle |
| title_full_unstemmed | Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle |
| title_short | Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle |
| title_sort | martelli chaotic properties of a generalized form of zadeh s extension principle |
| url | http://dx.doi.org/10.1155/2014/956467 |
| work_keys_str_mv | AT yaoyaolan martellichaoticpropertiesofageneralizedformofzadehsextensionprinciple AT chunlaimu martellichaoticpropertiesofageneralizedformofzadehsextensionprinciple |