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On fuzzifications of discrete dynamical systems
- Source :
-
Information Sciences . Jul2011, Vol. 181 Issue 13, p2858-2872. 15p. - Publication Year :
- 2011
-
Abstract
- Abstract: Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s Zadeh presented an extension principle helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets Syst. 61 (1994) 277–283] to generalize Zadeh’s original extension principle. In this paper we study basic properties of so-called g-fuzzifications, such as their continuity properties. We also show that, for any g-fuzzification: (i) a uniformly convergent sequence of uniformly continuous maps on X induces a uniformly convergent sequence of fuzzifications on the space of fuzzy sets and (ii) a conjugacy (resp., a semi-conjugacy) between two discrete dynamical systems can be extended to a conjugacy (resp., a semi-conjugacy) between fuzzified dynamical systems. Throughout this paper we consider different topological structures in the space of fuzzy sets, namely, the sendograph, endograph and levelwise topologies. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00200255
- Volume :
- 181
- Issue :
- 13
- Database :
- Academic Search Index
- Journal :
- Information Sciences
- Publication Type :
- Periodical
- Accession number :
- 59927806
- Full Text :
- https://doi.org/10.1016/j.ins.2011.02.024