On Fuzzy Rule Reduction Method Based On Data

As the amount of data in various fields continues to increase,the problem of data description and analysis has brought great challenges to people.Fuzzy inference system not only has high classification and prediction accuracy,but also can make human experts better grasp and understand the characteristics of the data set through the fuzzy inference system model because of its readability.Fuzzy inference system is a well compromise choice between the accuracy of the model and the readability of the model.Usually,when solving the modeling problem of low-dimensional nonlinear data,we can establish a fuzzy inference system with the help of experts to solve the problem.However,when there are many attribute variables,that is,the dimension of data is high,it is difficult for expert system to obtain accurate fuzzy rules.Therefore,people pay more and more attention to obtaining fuzzy rules from given data.In general,when the data with low dimensions,in order to make the prediction accuracy of the system reach the expected ideal range,as many fuzzy rules as possible are used in modeling.For data with high dimensions,retaining all fuzzy rules will increase the complexity of the system,and it is not easy to describe the system and interpret the fuzzy rules.Even for data with very high dimensions,the dimensionality disaster of fuzzy rules may occur,resulting in the failure of modeling and model parameter training.Fuzzy rule set is a core part of fuzzy inference system.Objectively,the number of fuzzy rules increases exponentially with the dimension of the data,which brings huge challenge to the construction of fuzzy inference systems through data.For the given sample data and fuzzy variables,how to extract fuzzy rules accurately and concisely is a core problem in the field of fuzzy inference system,and also a hot issue.Based on correspondence analysis theory,this paper studies the modeling of fuzzy inference system and the extraction of fuzzy rules based on data.And in the application of fuzzy inference system,we focus on predicting the price trend of financial products.The main work is as follows:1.With the theory and thought of correspondence analysis,the modeling problem of Takagi-Sugeno(T-S)fuzzy inference system is studied,and gives a T-S fuzzy inference system modeling algorithm based on correspondence analysis(TS-CAFM).In the traditional correspondence analysis method,the idea of“dimensionality reduction” is adopted to express the proportional structure of each category of attribute variables in the form of points in low dimensional space,which is generally two-dimensional space.Therefore,the corresponding relationship between “row point” and “column point” can be seen intuitively in the graph of low dimensional space.But at this time,the coordinate scales of “row points” and“column points” are different,so it is not feasible to cluster them by their coordinates.In this paper,correspondence analysis is carried out in the row profile space,so as to obtain effective fuzzy rules and establish a T-S fuzzy inference system.In addition,the proposed algorithm is compared with T-S type system based on fuzzy c-means(FCM)clustering,particle swarm optimization(PSO)and genetic algorithm(GA).From the experimental results,TS-CAFM algorithm can make the system achieve a balance between accuracy and complexity.2.A modeling algorithm of Mamdani fuzzy inference system based on correspondence analysis is proposed(Ma-CAFM).According to the characteristics of correspondence analysis that can identify the correspondence between input variables and output variables,fuzzy rules are obtained and Mamdani fuzzy inference system is established.When dealing with the regression problem,it is compared with the Mamdani fuzzy system based on FCM clustering.When dealing with classification problem,it is compared with the Mamdani fuzzy system based on grid clustering and subtractive clustering.Through the effect of simulation examples,it can be seen that Ma-CAFM algorithm can not only solve the regression problem well,but also accurately classify the data.3.Based on the fuzzy inference system,buying and selling strategies of stocks are studied.Aiming at the technical analysis tools of financial products such as moving average convergence and divergence(MACD),stochastics oscillator(KDJ)and directional movement index(DMI),fuzzy inference systems are established.The strategies of buying or selling financial products are given by fuzzy inference systems,including buying price and quantity,selling price and quantity and so on.The purpose of trading financial products is to avoid risks and make profits.It is more important to judge the trend of the price than to predict the accurate value of the price.Therefore,the validity of the presented model to be verified is not based on the prediction accuracy of stock prices,but on the profit obtained from simulated trading through the trading strategies given by the model in a period of time.Taking 15 stocks in the Shanghai and Shenzhen A-share market as an example,most of the stocks that are simulated by the system can get more profits in a period of time.