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中文摘要：
基于矩阵扰动理论,研究利用累积法估计GM（1,1）模型参数时解的稳定性问题。研究结果表明：累积的阶数越高,解的扰动界越大；在扰动值相等的情况下,新数据相比于老数据,解的扰动界较小；新数据对解的影响较小,这与新信息优先原理相矛盾。对此,提出分数阶累积法,当阶数小于1时,这种矛盾有所缓解,解的扰动界也较小。最后通过具体实例验证了分数阶累积法的实用性与可靠性。
英文摘要：
Based on the matrix perturbation theory, the stability problem of the solution to accumulating GM（1,1） is studied. The research results show that the larger the order of accumulating is, the larger the perturbation bound is, and the perturbation bound is smaller when the newer data is perturbed under the equal perturbation. The traditional grey integer order accumulate method leads to the solution to model, which is contradictory with the principle of new information priority, thus the fractional order accumulating method is proposed. The contradiction is relieved and the perturbation bound is becoming smaller when the order is less than 1. A real example demonstrates the practicability and reliability of the proposed method.
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