Research On Degree Of Grey Incidences Modeling Technology For Matrix Data

The grey relational analysis was an important part of grey system theory which study the uncertainty and poor information systems. Grey relational analysis(GRA) has been widely applied in system analysis, advantage analysis, data clustering, pattern identification and data mining. The application proved important academic and practical value of GRA. Although GRA theory has achieved many success, but there were still some imperfections.In the thesis, Multidimensional objects data description methods was discussed, more comprehensive multidimensional object behavior matrix theory was established. On the basis, matrix analysis axiom, property, modeling and application were studied deeply, with quantitative research and case study method.The main contents of this thesis were:First,application of grey relational analysis was extended,and the behavior matrix theory of multi-dimensional object was explored. The object of GRA was extended from behavior sequence to the behavior of matrix and matrix sequence. Then, The behavior matrix data structure, data size and the physical meaning were analyzed. Meanwhile behavior matrix initial operator, the starting zero operator, neighbor operator, data preprocessing and repair methods for behavior matrix also were disscussed. Last, behavior matrix and matrix sequence description methods were proposed, a comparatively perfect behavior matrix data model system was formed to lay the theoretical foundation for matrix GRA construction.Second, application scope of GRA models was extended by inheriting the basic thought of GAR. Some superior traditional model, for example: Deng-si, absolute, incidence and so on, were developed. On the basic idea of GRA, these models were extended to three-dimensional and four-dimensional data space, and these exeteded models were improved the general forms of the original ones for sequences. At the same time, parameters of general matrix incidence degree was optimized for improving the discrimination of analysis by the particle swarm algorithm, and GRA model for grey matrix aslo was constructed.Thired, adapting multidimensional objects data characteristics, some new matrix GRA models were constructed. Accroding to shortcomings of extended models, volume, normal vector and incremental incidence degree model were constructed depending on behavior of the local volume matrix, the behavior of the surface normal vector, and incremental vector feature. Then, proximity, similarity and comprehensive GRA models were study,,to form a more complete multidimensional data GRA model system.Forth, relational analysis axiom system was perfected, new GRA models'properties were studied deeply. The sequence relational analysis axioms, parallel, consistent and affine transform rank properties were extended to multidimensional space, then a complete matrix model axiom system and property framework were formed to guide and test models. In modeling, more attention was paid to the property research. These studies show that: Deng-si, absolute and volume matrix GRA models meet the requirements in parallel, gradient, ratios and similar models satisfied the consistency preperty. In particular, the gradient model,which meet parallel, consistency and invariance of affine transform perprety, was an excellent matrix GRA model. Fifth, With multi-sequence test data, model performance was compared. In order to test the performance of the models, and to compare merits of models objectively, three proposed proximity model was tested, their performance was recorded, and the results were compared with PCA and Euclid methods, in virtue of small-scale test data set REF multiple sequence and large-scale multi-sequence test data sets EEG which were commonly used in multivariate time series analysis. The results showed that: the volume and general matrix GRA models perform excellently in similarity analysis for small-scale matrix, so they were new method dealing with small-scale multidimensional data. But matrix GRA model performed weakly in large-scale data, and can not be directly used for large-scale behavior matrix.Sixth, more attention was paied to practice, and some challenges of management were solved. To solve multiple issues which were widespread in the economic management, the proposed matrix GRA model was applied to panel data analysis, financial multivariate time series analysis, dynamic multi-attribute decision making. The applications achieved better results, and solve the problem that the traditional methods of data analysis and decision-making method did not reflect the dynamicprocess.