Some Chaotic Properties of Discrete Fuzzy Dynamical Systems
Letting (X,d) be a metric space, f:X→X a continuous map, and (ℱ(X),D) the space of nonempty fuzzy compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the Zadeh's extension f̂:ℱ(X)→ℱ(X):u↦f̂u. In this paper, we present, as a response to the question proposed...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/875381 |
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| author | Yaoyao Lan Qingguo Li Chunlai Mu Hua Huang |
| author_facet | Yaoyao Lan Qingguo Li Chunlai Mu Hua Huang |
| author_sort | Yaoyao Lan |
| collection | DOAJ |
| description | Letting (X,d) be a metric space, f:X→X a continuous map, and (ℱ(X),D) the space of nonempty fuzzy compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the Zadeh's extension f̂:ℱ(X)→ℱ(X):u↦f̂u. In this paper, we present, as a response to the question proposed by Román-Flores and Chalco-Cano 2008, some chaotic relations between f and f̂. More specifically, we study the transitivity, weakly mixing, periodic density in system (X,f), and its connections with the same ones in its fuzzified system. |
| format | Article |
| id | doaj-art-d52406fc4b474e5098edfcfb364a74d8 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d52406fc4b474e5098edfcfb364a74d82025-08-20T03:19:42ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/875381875381Some Chaotic Properties of Discrete Fuzzy Dynamical SystemsYaoyao Lan0Qingguo Li1Chunlai Mu2Hua Huang3College of Computer Science, Chongqing University, Chongqing 401331, ChinaCollege of Applied Mathematics, Hunan University, Changsha 410082, Hunan, ChinaCollege of Computer Science, Chongqing University, Chongqing 401331, ChinaDepartment of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan 402160, ChinaLetting (X,d) be a metric space, f:X→X a continuous map, and (ℱ(X),D) the space of nonempty fuzzy compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the Zadeh's extension f̂:ℱ(X)→ℱ(X):u↦f̂u. In this paper, we present, as a response to the question proposed by Román-Flores and Chalco-Cano 2008, some chaotic relations between f and f̂. More specifically, we study the transitivity, weakly mixing, periodic density in system (X,f), and its connections with the same ones in its fuzzified system.http://dx.doi.org/10.1155/2012/875381 |
| spellingShingle | Yaoyao Lan Qingguo Li Chunlai Mu Hua Huang Some Chaotic Properties of Discrete Fuzzy Dynamical Systems Abstract and Applied Analysis |
| title | Some Chaotic Properties of Discrete Fuzzy Dynamical Systems |
| title_full | Some Chaotic Properties of Discrete Fuzzy Dynamical Systems |
| title_fullStr | Some Chaotic Properties of Discrete Fuzzy Dynamical Systems |
| title_full_unstemmed | Some Chaotic Properties of Discrete Fuzzy Dynamical Systems |
| title_short | Some Chaotic Properties of Discrete Fuzzy Dynamical Systems |
| title_sort | some chaotic properties of discrete fuzzy dynamical systems |
| url | http://dx.doi.org/10.1155/2012/875381 |
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