Grey Forecasting Model Based On Fuzzy Sets And Its Application

The GM(1,1)model proposed by Deng J L shows strong adaptability to the information mining for variation tendencies of complex systems.Since its proposal,improvements to the GM(1,1)model have never stopped.In terms of improving the predictive ability of the series,all the existing models till now have excellent performance to different degrees.However,the adaptability and prediction accuracy for any given approximately non-homogeneous exponential sequences are not satisfactory.To further enhance the predictive performance and generalization ability of the model,starting with the improvement of modeling ideas and methods,and combining with fuzzy set theory,this dissertation has explored the prediction model construction method for unascertained system.Main research points list as follows.(1)In order to enhance adaptability of grey prediction model to the any given sequence,Grey forecasting Model with Full Order Time Power terms,abbreviated as FOTPGM(1,1),is proposed.Firstly,parameter estimation,solving method,predictive attributes and relationship attributes compared with known models are investigated.Then,the structure variable mechanism by matching sequence through parameter pipeline is discussed,along with the proposal of visualization method for selecting optimal model structure.Afterwards,ill-posed problems and avoidance methods are analyzed.Compared with the traditional models,it shows that FOTP-GM(1,1)has higher prediction accuracy and stronger generalization ability.(2)In order to predict precisely the approximate nonhomogeneous exponential sequence with the perturbation terms of acceleration,velocity and constant,both models of VSSGM and VCGM are proposed,which are two special forms of the FOTP-GM(1,1)model.Then 5 typical sequences are utilized to test the prediction performance of these two models,and comparison is made among them and other known grey models.It is found that the VCGM model can achieve accurate simulation and unbiased prediction for approximately inhomogeneous exponential sequence with velocity and constant disturbance terms.Furthermore,VSSGM can predict accurately these kinds of sequences with acceleration disturbance term.(3)On the basis of R-fuzzy set and its membership rough approximation sets,the concept of advantage measure and related theoretical methods are proposed to solve the problem of how to find the optimal membership when the descriptive evaluation on object is known but its membership degree is unknown.The equivalence between the advantage measure and the type-1 fuzzy set is proved,and the equivalence between the type-2fuzzy set which takes advantage measure as its membership and R-fuzzy set is proved too.Then,the consistency of advantage measure with R-fuzzy set is proved,and it is pointed out that the essence of the advantage measure is the verifier of the R-fuzzy rough membership set.(4)To enhance the model's ability to track the changing sequences,MVCGM model characterized by metabolism is proposed based on new information priorities,and furthermore,ABC-MVCGM model is put forward by combining ABC algorithm with MVCGM model together to get optimal model parameters.The effects of dynamic performance,convergence and population size on ABC-MVCGM model are then analyzed.Based on the prediction and analysis of HLC,i.e.Heat Loss Capacity,which is a comprehensive indicator for spontaneous combustion of coal stockpile,one can get the conclusion that ABC-MVCGM has higher accuracy than other discussed models.(5)In order to improve the prediction accuracy of the original IGPM_T interval grey number prediction model,the GM(1,1)model which is the essential part of the original IGPM_T model is replaced by the proposed VSSGM model.By the improved IGPM_T model combined with the advantage measure for parameter identification,more accurate triangular fuzzy number and the resulting interval grey number sequence can be obtained.Afterwards,as two important influencing factors in investment decision for coal-fired power plant,the on-grid price and coal power cost are predicted successfully by the improved IGPM_T model.