Fuzzy sets theory cannot describe the data comprehensively, which has greatly limited the objectivity of fuzzy time series in uncertain data forecasting. In this regard, an intuitionistic fuzzy time series forecasting model is built. In the new model, a fuzzy clustering algorithm is used to divide the universe of discourse into unequal intervals, and a more objective technique for ascertaining the membership function and nonmembership function of the intuitionistic fuzzy set is proposed. On these bases, forecast rules based on intuitionistic fuzzy approximate reasoning are established. At last, contrast experiments on the enrollments of the University of Alabama and the Taiwan Stock Exchange Capitalization Weighted Stock Index are carried out. The results show that the new model has a clear advantage of improving the forecast accuracy.

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In existing fuzzy time series forecasting models, the accuracy of forecasting excessively relies on priori knowledge and output cannot effectively forecast multi values. The forecasting accuracy reduces drastically when time series data deviate from experience boundary in most models. The generalisation performance is insufficient. To overcome defects of traditional methods, this study proposed a long-term intuitionistic fuzzy time series (IFTS) forecasting model based on vector quantisation and curve similarity measure. In preprocessing of the proposed model, FTS theory is extended to long-term IFTS forecasting scope, the raw historical data are quantised vectors and optimum clustering centroids are searched by intuitionistic fuzzy c-means clustering algorithm. Curve similarity measure algorithm is proposed in procedure of forecasting, which avoids influence of mutation points and overcomes limitation of priori information. Euclidean distance is replaced by Fréchet distance, it is appropriate for such directed time series in vector matching. The proposed model and relevant models are implemented on three different datasets, a synthetic dataset, the monthly total retail sale of social consumer goods and daily mean temperature dataset. The forecasting results, index mean square error and average forecasting error rate indicate that our model performance better in different time series patterns than others.

To solve the problem of low accuracy and high false-alarm rate of existing intrusion detection models for multiple classifications of intrusion behaviors, a network intrusion detection model incorporating convolutional neural network and bidirectional gated recurrent unit is proposed. To solve the problems of many dimensions of features and imbalance of positive and negative samples in the original traffic data, sampling processing is performed with the help of a hybrid sampling algorithm combining ADASYN and RENN, and feature selection is performed by combining random forest algorithm and Pearson correlation analysis; after that, spatial features are extracted by the convolutional neural network, and further features are extracted by incorporating average pooling and max pooling, and then BiGRU is used to extracts long-distance dependent information features to achieve comprehensive and effective feature learning. Finally, the Softmax function is used for classification. In this paper, the proposed model is evaluated on the UNSW_NB15, NSL-KDD, and CIC-IDS2017 data sets with an accuracy of 85.55%, 99.81%, and 99.70%, which is 1.25%, 0.59%, and 0.27% better than the same type model of CNN-GRU.

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Network traffic anomaly detection is an important technology in cyberspace security. Combining information entropy theory and a variable ordering heuristic intuitionistic fuzzy time series forecasting model, we present a traffic anomaly detection algorithm based on intuitionistic fuzzy time series graph mining. For multi-dimensional attribute entropy of network traffic data, we establish multiple parallel and independent variable ordering heuristic intuitionistic fuzzy time series forecasting models. At each moment, using the multi-dimensional attribute entropy values as vertices, we construct complete graphs using amplitudes of the change in entropy values and edge weights between vertices defined by similarity, and establish an intuitionistic fuzzy time series graph of the traffic data in the time dimension. We perform frequent subgraph mining on the intuitionistic fuzzy time series graph; build the anomaly vectors based on the mining results, and implement adaptive determination for network traffic anomalies by fitting the anomaly vectors. Comparative experiments on universal datasets verify the superior performance of the algorithm. INDEX TERMS Intuitionistic fuzzy time series forecasting, information Entropy, graph mining, network traffic anomaly detection.

To enhance the accuracy of intuitionistic fuzzy time series forecasting model, this paper analyses the influence of universe of discourse partition and compares with relevant literature. Traditional models usually partition the global universe of discourse, which is not appropriate for all objectives. For example, the universe of the secular trend model is continuously variational. In addition, most forecasting methods rely on prior information, i.e., fuzzy relationship groups (FRG). Numerous relationship groups lead to the explosive growth of relationship library in a linear model and increase the computational complexity. To overcome problems above and ascertain an appropriate order, an intuitionistic fuzzy time series forecasting model based on order decision and adaptive partition algorithm is proposed. By forecasting the vector operator matrix, the proposed model can adjust partitions and intervals adaptively. The proposed model is tested on student enrollments of Alabama dataset, typical seasonal dataset Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and a secular trend dataset of total retail sales for social consumer goods in China. Experimental results illustrate the validity and applicability of the proposed method for different patterns of dataset.