Research On Time Series Data Prediction Based On Limited Penetrable Visibility Graph And Intuitionistic Fuzzy Set

Time series data refers to a set of data arranged in chronological order,which can be collected at predetermined time intervals such as natural days,weeks,months,quarters,etc.Time series contains observation data of time and corresponding times.By studying the relationship and variation patterns between observation values,time series can be modeled and future observation values can be predicted.At present,time series prediction has been applied in many fields,such as industrial production,atmospheric monitoring,financial analysis,etc.The primary task of studying time series is to analyze the properties of data and explore the structural characteristics of time series.With the deepening of network research,the connection between time series and networks has become increasingly close,and they have similar structures.By studying time series through network methods,the difficulty of data acquisition can be reduced while extracting the features of time series.The visibility graph proposed by Lacasa for the first time can convert time series into networks with nodes and edges.According to different visual rules,it can also be converted into horizontal visual graphs,finite traversal visual graphs,and so on.The converted network retains the fluctuation characteristics of the original sequence.By analyzing the topology of the network and exploring the similarity between nodes,it can provide convenience for time series prediction.In reality,due to sensor anomalies or unreasonable statistical methods,the observed values often have errors.Using traditional time series prediction methods to model uncertain time series can affect the final prediction accuracy.When dealing with the uncertainty of time series,it is not only necessary to consider the data itself,but also factors such as model selection and parameter estimation.Intuitive fuzzy sets use membership functions,non membership functions,and hesitation indices to represent uncertain information.By formulating reasonable fuzzy rules and intuitionistic fuzzy reasoning,uncertain data can be effectively processed.Therefore,applying Intuitionistic fuzzy set to time series analysis can improve prediction accuracy.This thesis takes time series prediction as the research object,explores the prediction of links and the processing of uncertain data,and proposes two time series prediction models.The main research content is as follows:(1)Time series prediction model based on restart random walk: use limited penetrable visibility graph to transform the time series into a network,analyze the time series through the network,make link prediction,calculate the similarity between the last known node and the rest of the nodes,and linearly fit the first largest similarity node with the last known node to obtain the preliminary prediction value,Finally,the preliminary predicted values are corrected based on the degree and distance of the nodes.(2)A time series prediction model based on intuitionistic fuzzy sets: intuitionistic fuzzy inference is set as the weighted sum of traditional fuzzy inference,and the influence of nodes on the prediction results is divided into primary and secondary influences.The primary influence reflects the tightness between nodes,and the secondary influence reflects the historical information contained in nodes.Design intuitionistic fuzzy set and fuzzy rules based on the distance between nodes,obtain the weights of the two influences through intuitionistic fuzzy reasoning,and sum the weights to obtain the final prediction result.(3)Experiment and analysis: The model proposed in this article is applied to predict the daily number of new infections of the Omicron virus and the Shanghai Composite Index in the United States,and compared with traditional time series prediction models and neural network prediction models.It is shown that the model in this article has better prediction performance when predicting time series with fewer training sets and seasonality.At the same time,by predicting the cumulative number of cured individuals and deaths,relevant guidance has been provided for epidemic prevention in China.(4)Design and implementation of a predictive message push system: With the opening of epidemic control,residents are facing significant infection risks.Based on the above research,the system can develop intuitive fuzzy inference rules and obtain inference results.The epidemic prediction results can be sent individually or in groups through SMS or email to improve residents’ awareness of epidemic prevention.The system can also push high-value data such as stock values.