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Jardon, D., Sanchez, I.. (1400). Sensitivity and strong sensitivity on induced dynamical systems. نشریه علمی دانشگاه سیستان و بلوچستان, 18(4), 69-78. doi: 10.22111/ijfs.2021.6177
D. Jardon; I. Sanchez. "Sensitivity and strong sensitivity on induced dynamical systems". نشریه علمی دانشگاه سیستان و بلوچستان, 18, 4, 1400, 69-78. doi: 10.22111/ijfs.2021.6177
Jardon, D., Sanchez, I.. (1400). 'Sensitivity and strong sensitivity on induced dynamical systems', نشریه علمی دانشگاه سیستان و بلوچستان, 18(4), pp. 69-78. doi: 10.22111/ijfs.2021.6177
Jardon, D., Sanchez, I.. Sensitivity and strong sensitivity on induced dynamical systems. نشریه علمی دانشگاه سیستان و بلوچستان, 1400; 18(4): 69-78. doi: 10.22111/ijfs.2021.6177

Sensitivity and strong sensitivity on induced dynamical systems

Iranian Journal of Fuzzy Systems
دوره 18، شماره 4، مهر و آبان 2021، صفحه 69-78    اصل مقاله (373.52 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2021.6177
نویسندگان
D. Jardon* 1؛ I. Sanchez2
1Academia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa S/N, Col. Lomas de Zaragoza 09620, Mexico City, Mexico.
2Departamento de Matematicas, Universidad Autonoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, Mexico City, Mexico
چکیده
Given a metric space X, we consider the family of all normal upper semicontinuous fuzzy sets on X, denoted by $\mathcal{F}(X)$, and a discrete dynamical system $(X,f)$. In this paper, we study when $(\mathcal{F}(X), \widehat{f})$ is (strongly) sensitive, where $\widehat{f}$ is the Zadeh's extension of f and $\mathcal{F}(X)$ is equipped with different metrics: The uniform metric, the Skorokhod metric, the sendograph metric and the endograph metric. We prove that the sensitivity in the induced dynamical system $(\mathcal{K}(X),\overline{f})$ is equivalent to the sensitivity in $ \widehat{f} :\mathcal{F}(X)\to \mathcal{F}(X) $ with respect to the uniform metric, the Skorokhod metric and the sendograph metric. We also show that the following conditions are equivalent:
\item {\rm a)} $(X,f)$ is strongly sensitive;
\item {\rm b)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the uniform metric;
\item {\rm c)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the Skorokhod metric;
\item {\rm d)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the sendograph metric.
کلیدواژه‌ها
Fuzzy set؛ Skorokhod metric؛ uniform metric؛ endograph metric؛ sendograph metric؛ Zadeh's extension؛ sensitive properties
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