Studies on Parameter Identification Using Fuzzy Random Data

本研究从模糊随机现象的一致性观点出发，引入了一类模糊随机向量及其统计矩，并从理论上研究了模糊随机向量及其统计矩的一些性质.模糊集的集合表示被充分采用，因为它可以描述FRVC之间的操作.通过采用紧凸对应族作为FRVC的集合表示，我们已经能够引入FRVC期望的合理定义，它基本上与Kwakernaak提出的（标量）模糊随机变量相容，并且从未从它们的简单扩展中获得. FRVC作为随机向量的模糊感知的概念的提出，在某种意义上可以作为两种主要的模糊mndoin变量之间的桥梁。FRVC高阶统计矩的定义及其估计量.在更温和的条件下，FRd3的统计特性。该方法在模糊随机数据中的应用，这些模糊随机数据是通过对AR、MA和阿尔马模型描述的时间序列的输出过程的模糊感知而获得的.用模糊随机数据辨识上述时间序列模型的系统参数。

In this research, a class of fuzzy random vectors(FRVCs) and their statistical moments have been introduced from the consistent viewpoint of vague perceptions of random phenomena, and some properties of FRVCs and their statistical moments up to second ones have been examined theoretically.The features of proposed FRVCs are as follows :1. Set representations of fuzzy sets are thoroughly adopted because of ilie feasibility for describing operations between FRVCs.2. By adopting the family of compact convex correspondences as the set representation of a FRVCS, we have been able to introduce the reasonable definition of expectations of FRVCs, which is basically compatible with (scalar) fuzzy random variables proposed by Kwakernaak and is never obtained from their simple extensions.3. The proposed concept of FRVCs as vague perceptions of random vectors may be, in some sense, a bridge between two major types of flizzy mndoin variables.Furthermore, the following items should be investigated in the future :1. Definitions of higher statistical moments of FRVCs and their estimators.2. Statistical properties of FRVCS under more moderate conditions3. Applications of the proposed approach to fuzzy random data obtained by vague perceptions of output processes of time series described by AR, MA and ARMA models and so on.4. Identification of system parameters of time series models as mentioned above bv using fuzzy random data.