Grey Prediction Modeling And Its Application Based On Interval Grey Numbers

With the social development,the concept of Big Data has been more and more mentioned.However,large data set,in which the effective information is very limited,often shows a short-term pattern and long-term disturbances in a rapidly changing environment which makes it difficult to use long data sequence of real numbers to express.By this means,grey system theory(GST)is introduced to analyze uncertain systems of "small data and limited information".In this thesis,interval grey numbers are taken as research objects and grey models based on interval grey numbers are constructed by grey generation technology,grey relational analysis and grey prediction methods.The established models are applied to the analysis of the complex system of regional traffic congestion in the Yangtze River Delta region.The main research work and results are as follows:(1)Optimize the combination function transformation technique based on interval grey numbers.Dealing with the problem of limited adjustment range of single function transformation method,the adjustable combination of function transformation methods are established by tangent or cotangent function as main composition which can improve the smooth ratio,compress class ratio and remain the "convex" feature of the data sequence.According to different trends of increasing sequences or decreasing sequences based on interval grey numbers respectively,novel grey prediction models based on combination function transformation are established based on the lower and upper bound sequences or the kernel and measure sequences of the interval grey numbers.(2)Construct grey prediction models of typical interval grey numbers.Based on grey degree information contained in interval grey numbers,a novel grey model of interval grey numbers based on the axiom of “non-decrease grey degree” is established by determining grey factors in which the axiom of of “non-decrease grey degree” is embodied in the whole process of modeling and the prediction values of the upper and lower bounds sequences of the interval grey number sequences are corrected.On the other hand,according to the similar residual characteristics in the kernel and the information domain sequences of interval grey number sequences,which is formed by the system behavior sequence and residual sequence,an optimized grey prediction model of interval grey numbers based on residual corrections is proposed by proposing the prediction models of the kernel sequence and extending the upper and lower bound information domainsequences with the residual error correction idea.The precision of the prediction is optimized and the principle of "full use of information" is embodied during the modeling process.(3)Propose grey prediction model based on the interval grey numbers with central points.For the interval grey numbers with central points,the non-homogeneous discrete grey models are established respectively by information transformations of the trapezoidal area sequence between the upper bound sequence and the central sequence,the trapezoidal area sequence between the lower bound sequence and the central sequence and the central line between the upper and lower bound sequences.Furthermore,through the initial condition optimization,the fitting accuracy of the prediction model has been improved based on the global thinking of fitting data.(4)Establish grey comprehensive relational prediction model based on interval grey numbers.In view of the complexity of multivariable interval grey number sequences,the information of area differences and slope cumulative deviations from different upper and lower bound of interval grey number sequences are considered in relational models which not only represent relative quantities but also characterize development speeds of relational sequences.In addition,the relational degree algorithm is optimized which improves the resolution of the traditional grey relational degree.According to the relational results,the multivariable grey model is proposed to forecast the main interval grey number sequence.(5)The study of regional traffic congestion in the Yangtze River Delta by using novel grey models.First,the general situation of the Yangtze River Delta and the increasing pressure of regional traffic are introduced.By collecting data of the indexes related to the regional traffic congestion,the upper and lower bound sequences of the interval grey numbers which represents the maximum level and lowest level in the region are extracted.Using combination function transformation technique,single variable grey prediction model and multivariable grey comprehensive relational model based on interval grey numbers,the key factors of the upper and lower bound data related to traffic congestion are identified and the multivariate forecasting model is established to predict the future traffic congestion trends in this region.