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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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آمار تعداد مشاهده مقاله: 600 تعداد دریافت فایل اصل مقاله: 481 |
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