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Why grey model is suitable for small sample is explained. Take discrete grey model as an example, based on matrix perturbation theory, we prove that the larger sample, the bigger perturbation bound and the smaller sample, the smaller perturbation bound under the equal perturbation when we use the traditional grey first order accumulate. The fractional order accumulate grey model is defined in order to reduce perturbation bound and its availability and practicality are verified by an example. [ABSTRACT FROM AUTHOR]

The convexity, concavity and the relative convexity of positive discrete series are denned, on this basis, the proximity of relative convexity among relevant factors is used to measure relation degree, we present the novel grey convex relation degree, the properties of the grey convex relation degree are discussed. We also put forward the independence from interference factors of the order of grey relations, and point out that the convex relation and other 6 kinds of grey relation degree satisfy the independence from interference factors, the grey relation degree put forward by Julong Deng could not satisfy the independence from interference factors. An example is given to illustrate that the grey convex relation degree can more really reflect the correlation degree among relevant factors sequences. [ABSTRACT FROM AUTHOR]