Research On Design Method Of Deep Stack Fuzzy System

As an important branch of computational intelligence,fuzzy systems have been gradually applied to industrial production and people's lives.However,when the fuzzy system is used to model a complex system,especially when the input variables increase,the fuzzy rules of classical fuzzy system also increase,which makes the construction of the model difficult.At present,to tackle this problem,a single-input-rule-modules connected fuzzy system was proposed by researchers,which makes the fuzzy rules increase linearly with the increase of input variables,greatly reducing the number of fuzzy rules and it is easy to design,and has been applied it to complex system modeling problems.However,the single-input-rule-modules connected fuzzy system is simply constructed by connecting the fuzzy modules.The module is too simple and the structure complexity is reduced,so the model's performance usually does not meet the expectations.Therefore,the new modular fuzzy systems are needed to reduce the difficulty of model design and to improve model's performance.In order to achieve the above goals,this paper proposes the architecture and design method of the stacked deep fuzzy system.The main contributions of this paper are as follows:(1)The double-input-rule-modules(DIRMs)stacked deep fuzzy design method is proposed.This method stacks the DIRMs bottom-up,layer-by-layer to construct a deep fuzzy model(DIRM-DFM).Its double-input-rule-module(DIRM)ensures the interpretability of the model.In the process of model construction,the DIRM parameter optimization strategy based on the constrained least squares method is given to ensure the learning speed and approximation performance of DIRM-DFM.In order to verify the performance of DIRM-DFM,it was applied to two time series forecasting problems which are the photovoltaic power generation and forecasting the subway passenger flow,and it is compared with shallow model adaptive fuzzy inference system(ANFIS),single-input-rule-module connected fuzzy system(SIRM-FM),function weight single-input-rule-module connected fuzzy system(FWSIRM-FM),deep model stack autoencoder(SAE)and deep convolutional fuzzy system(DCFS).Experimental results show that the proposed DIRM-DFM is optimal in terms of the prediction accuracy and the stability of the prediction results.(2)In order to further compress the model's structure,the subtractive clustering double-input-rule-modules stacked deep fuzzy design method is proposed.This method adopts the same stacking strategy as DIRM-DFM to build a deep fuzzy model(SCMDIRM-DFM),but in its construction process,a subtractive clustering algorithm is used to construct each double-input-rule-module.The subtractive clustering strategy can greatly reduce the number of fuzzy rules in each fuzzy module and the model structure can be compressed.Similarly,experiments and comparisons forecasting are carried out in the same two time series forecasting problems which are the photovoltaic power generation and the subway passenger flow.Experimental results demonstrate that,after compressing the model's structure,the prediction accuracy of the SCMDIRM-DFM is equivalent to that of DIRM-DFM,but there exist much fewer fuzzy rules.In addition,its prediction performance is better than other comparison models.(3)In order to further improve the model's ability to deal with uncertainty and improve prediction performance,an interval type-2 double-input-rule-module(IT2DIRM)stacked deep fuzzy design method is proposed.The IT2 DIRM stacked deep fuzzy model(IT2DIRM-DFM)constructed by this method is based on the DIRM-DFM,but one stack layer is added.This layer reuses the worst-performing IT2 DIRM,so that the width and depth of the IT2DIRM-DFM become adaptive,which lead to the higher degree of design freedom.In the process of this model's construction,the constrained least squares method is used to optimize the subsequent parameters of each IT2 DIRM to ensure that the constructed IT2DIRM-DFM has good prediction performance.The IT2DIRM-DFM model has also been applied and verified in the same two time series forecasting problems.Experimental results verified that,compared with other comparison models,the IT2DIRM-DFM model has the highest prediction accuracy and the most stable prediction results.