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題名 Fuzzy/Probability~Fractal/Smooth
作者 吳柏林
關鍵詞 Multi-D degrees of belief; fractal; fuzzy; probability
日期 1999
上傳時間 12-Nov-2010 12:16:47 (UTC+8)
摘要 Many applications of probability theory are based on the assumption that, as the number of cases increase, the relative frequency of cases with a certain property tends to a number – probability that this property is true. L. Zadeh has shown that in many real-life situations, the frequency oscillates and does not converge at all. It is very difficult to describe such situations by using methods from traditional probability theory. Fuzzy logic is not based on any convergence assumptions and therefore, provides a natural description of such situations. However, a natural next question arises: how can we describe this oscillating behavior? Since we cannot describe it by using a single parameter (such as probability), we need to use a multi-D formalism. In this paper, we describe an optimal formalism for describing such oscillations, and show that it complements traditional probability techniques in the same way as fractals complement smooth curves and surfaces.
關聯 International Journal of Uncertainty Fuzziness and Knowledge - Based Systems,7(4),363-370
資料類型 article
DOI http://dx.doi.org/10.1142/S0218488599000313
dc.creator (作者) 吳柏林zh_TW
dc.date (日期) 1999-
dc.date.accessioned 12-Nov-2010 12:16:47 (UTC+8)-
dc.date.available 12-Nov-2010 12:16:47 (UTC+8)-
dc.date.issued (上傳時間) 12-Nov-2010 12:16:47 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/48302-
dc.description.abstract (摘要) Many applications of probability theory are based on the assumption that, as the number of cases increase, the relative frequency of cases with a certain property tends to a number – probability that this property is true. L. Zadeh has shown that in many real-life situations, the frequency oscillates and does not converge at all. It is very difficult to describe such situations by using methods from traditional probability theory. Fuzzy logic is not based on any convergence assumptions and therefore, provides a natural description of such situations. However, a natural next question arises: how can we describe this oscillating behavior? Since we cannot describe it by using a single parameter (such as probability), we need to use a multi-D formalism. In this paper, we describe an optimal formalism for describing such oscillations, and show that it complements traditional probability techniques in the same way as fractals complement smooth curves and surfaces.-
dc.language zh_TWen
dc.language.iso en_US-
dc.relation (關聯) International Journal of Uncertainty Fuzziness and Knowledge - Based Systems,7(4),363-370en
dc.subject (關鍵詞) Multi-D degrees of belief; fractal; fuzzy; probability-
dc.title (題名) Fuzzy/Probability~Fractal/Smoothen
dc.type (資料類型) articleen
dc.identifier.doi (DOI) 10.1142/S0218488599000313-
dc.doi.uri (DOI) http://dx.doi.org/10.1142/S0218488599000313-