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政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/48302

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/48302

Title:	Fuzzy/Probability~Fractal/Smooth
Authors:	吳柏林
Keywords:	Multi-D degrees of belief;fractal;fuzzy;probability
Date:	1999
Issue Date:	2010-11-12 12:16:47 (UTC+8)
Abstract:	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.
Relation:	International Journal of Uncertainty Fuzziness and Knowledge - Based Systems,7(4),363-370
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1142/S0218488599000313
DOI:	10.1142/S0218488599000313
Appears in Collections:	[應用數學系] 期刊論文

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