کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
394222 | 665785 | 2011 | 15 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On fuzzifications of discrete dynamical systems On fuzzifications of discrete dynamical systems](/preview/png/394222.png)
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.
Journal: Information Sciences - Volume 181, Issue 13, 1 July 2011, Pages 2858–2872