Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system

Cloud Model-Based Adaptive Time-Series Information Granulation Algorithm and Its Similarity Measurement

To efficiently reduce the dimensionality of time series and enhance the efficiency of subsequent data-mining tasks, this study introduces cloud model theory to propose a novel information granulation method and its corresponding similarity measurement. First, we present an information granulation validity index of time series (IGV) based on the entropy and expectation of the cloud model. Taking IGV as the granulation target for time series, an adaptive information granulation algorithm for time series (CMAIG) is proposed, which can transform a time series into a granular time series consisting of several normal clouds without pre-specifying the number of information granules, achieving efficient dimensionality reduction. Then, a new similarity measurement method (CMAIG_ECM) is designed to calculate the similarity between two granular time series. Finally, the hierarchical clustering algorithm based on the proposed time series information granulation method and granular time series similarity measurement method (CMAIG_ECM_HC) is carried out on some UCR datasets and a real stock dataset, and experimental studies demonstrate that CMAIG_ECM_HC has superior performance in clustering time series with different shapes and trends.

Linear Fuzzy Information-Granule-Based Fuzzy C-Means Algorithm for Clustering Time Series

This article aims to design a trend-oriented-granulation-based fuzzy C -means (FCM) algorithm that can cluster a group of time series at an abstract (granular) level. To achieve a better trend-oriented granulation of a time series, l1 trend filtering is firstly carried out to result in segments which are then optimized by the proposed segment merging algorithm. By constructing a linear fuzzy information granule (LFIG) on each segment, a granular time series which well reflects the linear trend characteristic of the original time series is produced. With the novel designed distance that can well measure the trend similarity of two LFIGs, the distance between two granular time series is calculated by the modified dynamic time warping (DTW) algorithm. Based on this distance, the LFIG-based FCM algorithm is developed for clustering time series. In this algorithm, cluster prototypes are iteratively updated by the specifically designed granule splitting and merging algorithm, which allows the lengths of prototypes to change in the process of iteration. This overcomes the serious drawback of the existing approaches, where the lengths of prototypes cannot be changed. Experimental studies demonstrate the superior performance of the proposed algorithm in clustering time series with different shapes or trends.

Fuzzy inference-based LSTM for long-term time series prediction

Long short-term memory (LSTM) based time series forecasting methods suffer from multiple limitations, such as accumulated error, diminishing temporal correlation, and lacking interpretability, which compromises the prediction performance. To overcome these shortcomings, a fuzzy inference-based LSTM with the embedding of a fuzzy system is proposed to enhance the accuracy and interpretability of LSTM for long-term time series prediction. Firstly, a fast and complete fuzzy rule construction method based on Wang-Mendel (WM) is proposed, which can enhance the computational efficiency and completeness of the WM model by fuzzy rules simplification and complement strategies. Then, the fuzzy prediction model is constructed to capture the fuzzy logic in data. Finally, the fuzzy inference-based LSTM is proposed by integrating the fuzzy prediction fusion, the strengthening memory layer, and the parameter segmentation sharing strategy into the LSTM network. Fuzzy prediction fusion increases the network reasoning capability and interpretability, the strengthening memory layer strengthens the long-term memory and alleviates the gradient dispersion problem, and the parameter segmentation sharing strategy balances processing efficiency and architecture discrimination. Experiments on publicly available time series demonstrate that the proposed method can achieve better performance than existing models for long-term time series prediction.

Entropy and probability based Fuzzy Induced Ordered Weighted Averaging operator

The traditional Ordered Weighting Average (OWA) operator is suitable for aggregating numerical attributes. However, this method fails when the attribute values are given in a linguistic form. In this paper, a novel aggregating method named Entropy and Probability based Fuzzy Induced Ordered Weighted Averaging (EPFIOWA) is proposed for Gaussian-fuzzy-number-based linguistic attributes. A method is first designed to obtain a reasonable weighting vector based on probability distribution and maximal entropy. Such optimal weighting vectors can be obtained under any given level of optimism, and the symmetric properties of the proposed model are proven. The linguistic attributes of EPFIOWA are represented by Gaussian fuzzy numbers because of their concise form and good operational properties. In particular, the arithmetic operations and distance measures of Gaussian fuzzy numbers required by EPFIOWA are given systematically. A novel method to obtain the order-inducing variables of linguistic attribute values is proposed in the EPFIOWA operators by calculating the distances between any Gaussian fuzzy number and a set of ordered grades. Finally, two numerical examples are used to illustrate the proposed approach, with evaluation results consistent with the observed situation.

Establish a trend fuzzy information granule based short-term forecasting with long-association and k-medoids clustering

In the existing short-term forecasting methods of time series, two challenges are faced: capture the associations of data and avoid cumulative errors. For tackling these challenges, the fuzzy information granule based model catches our attention. The rule used in this model is fuzzy association rule (FAR), in which the FAR is constructed from a premise granule to a consequent granule at consecutive time periods, and then it describes the short-association in data. However, in real time series, another association, the association between a premise granule and a consequent granule at non-consecutive time periods, frequently exists, especially in periodical and seasonal time series. While the existing FAR can’t express such association. To describe it, the fuzzy long-association rule (FLAR) is proposed in this study. This kind of rule reflects the influence of an antecedent trend on a consequent trend, where these trends are described by fuzzy information granules at non-consecutive time periods. Thus, the FLAR can describe the long-association in data. Correspondingly, the existing FAR is called as fuzzy short-association rule (FSAR). Combining the existing FSAR with FLAR, a novel short-term forecasting model is presented. This model makes forecasting at granular level, and then it reduces the cumulative errors in short-term prediction. Note that the prediction results of this model are calculated from the available FARs selected by the k-medoids clustering based rule selection algorithm, therefore they are logical and accurate. The better forecasting performance of this model has been verified by comparing it with existing models in experiments.

Implement multi-step-ahead forecasting with multi-point association fuzzy logical relationship for time series

In the existing high-order fuzzy logical relationship (FLR) based forecasting model, each FLR is used to describe the association between multiple premise observations and a consequent observation. Therefore, these FLRs concentrate on the one-step-ahead forecasting. In real applications, there exist another kind of association: the association between multiple premise observations and multiple consequent observations. For such association, the existing FLRs can’t express and ignored. To depict it, the high-order multi-point association FLR is raised in this study. The antecedent and consequent of a high-order multi-point association FLR are consisted of multiple observations. Thus, the proposed FLR reflects the influence of multiple premise observations on the multiple consequent observations, and can be applied for multi-step-ahead forecasting with no cumulative errors. On the basis of high-order multi-point association FLR, the high-order multi-point trend association FLR is constructed, it describes the trend association in time series. By using these two new kinds of FLRs, a fuzzy time series based multi-step-ahead forecasting model is established. In this model, the multi-point (trend) association FLRs effective in capturing the associations of time series and improving forecasting accuracy. The benefits of the proposed FLRs and the superior performance of the established forecasting model are demonstrated through the experimental analysis.

An interval fuzzy number-based fuzzy collaborative forecasting approach for DRAM yield forecasting

Most existing fuzzy collaborative forecasting (FCF) methods adopt type-1 fuzzy numbers to represent fuzzy forecasts. FCF methods based on interval-valued fuzzy numbers (IFNs) are not widely used. However, the inner and outer sections of an IFN-based fuzzy forecast provide meaning information that serves different managerial purposes, which is a desirable feature for a FCF method. This study proposed an IFN-based FCF approach. Unlike existing IFN-based fuzzy association rules or fuzzy inference systems, the IFN-based FCF approach ensures that all actual values fall within the corresponding fuzzy forecasts. In addition, the IFN-based FCF approach optimizes the forecasting precision and accuracy with the outer and inner sections of the aggregation result, respectively. Based on the experimental results, the proposed FCF-II approach surpassed existing methods in forecasting the yield of a dynamic random access memory product.

Intuitionistic fuzzy time series functions approach for time series forecasting

Fuzzy inference systems have been commonly used for time series forecasting in the literature. Adaptive network fuzzy inference system, fuzzy time series approaches and fuzzy regression functions approaches are popular among fuzzy inference systems. In recent years, intuitionistic fuzzy sets have been preferred in the fuzzy modeling and new fuzzy inference systems have been proposed based on intuitionistic fuzzy sets. In this paper, a new intuitionistic fuzzy regression functions approach is proposed based on intuitionistic fuzzy sets for forecasting purpose. This new inference system is called an intuitionistic fuzzy time series functions approach. The contribution of the paper is proposing a new intuitionistic fuzzy inference system. To evaluate the performance of intuitionistic fuzzy time series functions, twenty-three real-world time series data sets are analyzed. The results obtained from the intuitionistic fuzzy time series functions approach are compared with some other methods according to a root mean square error and mean absolute percentage error criteria. The proposed method has superior forecasting performance among all methods.