Fuzzy Granulation Research Articles

Integrating granular computing with density estimation for anomaly detection in high-dimensional heterogeneous data

Detecting anomalies in complex data is crucial for knowledge discovery and data mining across a wide range of applications. While density-based methods are effective for handling varying data densities and diverse distributions, they often struggle with accurately estimating densities in heterogeneous, uncertain data and capturing interdependencies among features in high-dimensional spaces. This paper proposes a fuzzy granule density-based anomaly detection algorithm (GDAD) for heterogeneous data. Specifically, GDAD first partitions high-dimensional attributes into subspaces based on their interdependencies and employs fuzzy information granules to represent data. The core of the method is the definition of fuzzy granule density, which leverages local neighborhood information alongside global density patterns and effectively characterizes anomalies in data. Each object is then assigned a fuzzy granule density-based anomaly factor, reflecting its likelihood of being anomalous. Through extensive experimentation on various real-world datasets, GDAD has demonstrated superior performance, matching or surpassing existing state-of-the-art methods. GDAD's integration of granular computing with density estimation provides a practical framework for anomaly detection in high-dimensional heterogeneous data.

Modeling methods for deep fuzzy inference systems based on feature selection

A bottom-up, layer-by-layer feature selection modeling method is proposed for deep fuzzy inference systems. By selecting features in the input space, redundant and interfering features in each layer's input space can be removed. The selected features have been appropriately ordered to avoid the randomness of features within the feature sliding window. Based on fuzzy rough set theory, the matching degree between the fuzzy granules associated with the conditional feature set and those associated with the decision feature is used as a likelihood function. The λ-AIC criterion with a penalty term have been redefined as an evaluation index for features. The obtained model is compared to four baseline models and an existing deep fuzzy rule classification system. The results show that the feature selection-based deep fuzzy inference system effectively improves data classification performance and efficiency. Compared to four rough set-based feature selection methods based on different measures, the method proposed is more convincing in terms of accuracy and the number of features selected. Compared to the modeling method where input space features are randomly shuffled, the feature sorting modeling method performs better and avoids the instability in model accuracy caused by randomness.

A novel combined wind speed forecasting system based on fuzzy granulation and multi-objective optimization

With the increasing application of wind energy, reliable wind speed prediction has become imperative. However, prior studies predominantly concentrated on single-model predictions, disregarding the inherent uncertainty in wind speed. This oversight resulted in inadequate deterministic and probabilistic forecasting outcomes across varying scenarios. To make up for these shortcomings, a novel forecasting system combining a data preprocessing technique, a sub-model selection method, and a modified multi-objective integrate optimization strategy is designed in this paper. According to the data obtained from China's wind farm, the forecasting efficiency of this system is verified from multiple perspectives. The findings show that the system takes advantage of each model to boost the precision and stability of point prediction successfully. Furthermore, it achieves higher interval coverage and narrower interval width under distinct confidence levels. These results highlight the system's potential as a reliable technical support for efficient dispatching of the entire power system.

A structure for predicting wind speed using fuzzy granulation and optimization techniques

A structure for predicting wind speed using fuzzy granulation and optimization techniques

A dynamic three-way conflict analysis model with adaptive thresholds

Three-way conflict analysis model, based on information systems, is about trisecting, getting coalitions and decision-making. Since the model is proposed by Yao, many models have been proposed to enrich the field of three-way conflict analysis. In this paper, we propose a new three-way conflict analysis model. Our work can be divided into four parts. First, we define new fuzzy granules and an new approximation operator to obtain better trisections. Second, we introduce dynamic information systems which are generalizations of classical information systems. The new information systems enable us to induce trisections dynamically. Third, a new Bayesian algorithm is proposed for thresholds-computing which plays an important role in inducing trisections. In the classical Bayesian approach, there are six original parameters given subjectively. And in our algorithm, the parameters are replaced by three centers and a distance measure. Finally, our new model is applied to tourism planning in two cases, one can be presented by a dynamic information system and the other one can be presented by a dispersed information system generalized from dynamic information system.

Fusing multi-scale fuzzy information to detect outliers

Outlier detection aims to find objects that behave differently from the majority of the data. Existing unsupervised approaches often process data with a single scale, which may not capture the multi-scale nature of the data. In this paper, we propose a novel information fusion model based on multi-scale fuzzy granules and an unsupervised outlier detection algorithm with the fuzzy rough set theory. First, a multi-scale information fusion model is formulated based on fuzzy granules. Then we employ fuzzy approximations to define the outlier factor of multi-scale fuzzy granules centered at each data point. Finally, the outlier score is calculated by aggregating the outlier factors of a set of multi-scale fuzzy granules. Experimental results demonstrate that the proposed method is comparable with or better than the leading outlier detection methods. The codes and datasets are publicly available online at https://github.com/ChenBaiyang/MFIOD.

Consistent Matrix: A Feature Selection Framework for Large-Scale Datasets

Large-scale data processing based on limited computing resources has always been a difficult problem in data mining, where feature selection is often used as an effective data compressing mechanism. For granular computing of big data, discernibility matrix and dependency degree are the most representative methods for matrix-based and feature importance degree-based feature selection, respectively. However, their temporal and space complexities are high and often lead to poor performance. In this paper, a novel feature selection framework for large scale data processing with linear complexities was proposed for the first time. Firstly, a much more concise fuzzy granule set, called fuzzy arithmetic covering, was introduced to reduce computational costs. Then a new matrix-based feature selection framework, namely consistent matrix, was proposed for general rough set models. As a result, a heuristic attribute reduction algorithm, i.e., HARCM, was designed accordingly. Compared with six state-of-the-art algorithms for feature selection, the average running time of the newly proposed algorithm was reduced up to 2913 times, with a comparable or even better classification performance.

Multi-class granular approximation by means of disjoint and adjacent fuzzy granules

In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute space (adjacent granules). Later, we consider granular approximations for multi-class classification problems leading to the definition of a multi-class granular approximation. Finally, we show how to efficiently calculate multi-class granular approximations for Łukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts.

NFIG-X: Nonlinear Fuzzy Information Granule Series for Long-Term Traffic Flow Time-Series Forecasting

Long-term time series forecasting is an extensive research topic and is of great significance in many fields. However, the task of long-term time series forecasting is accompanied by the problem of increasing cumulative error and decreasing time correlation. To overcome these shortcomings, this work proposes a prediction framework based on non-linear fuzzy information granule (NFIG) series, which can boost the long-term performance of most predictors. Firstly, we propose the representation of NFIG for the first time, replacing the linear core lines with non-linear time-dependent curves. Secondly, we propose a temporal window splitting algorithm based on curvature equations and weighted directed graphs, which can not only merge temporal windows with the same trend but also cointegrate incremental data. Finally, the non-linear trend fuzzy granulation can be employed as a data preprocessing module for various time series predictors to achieve better long-term forecasting performance. As a typical time series forecasting task, the precise long-term forecast of traffic flow data can relieve the overburdened traffic system and improve the traffic environment to a certain extent. Thus, the proposed method is employed for long-term traffic flow forecasting. Compared with existing forecasting models, which achieves superior performances.

Incremental nonlinear trend fuzzy granulation for carbon trading time series forecast

In addition to its important economic value, carbon trading is also an important tool in international politics and diplomacy. Carbon price forecast accuracy has far-reaching implications for economic development and the environment. Few existing studies have been more accurate in predicting carbon prices over longer periods. In this paper, the incremental Gaussian nonlinear trend fuzzy granulation method and the Gaussian nonlinear trend fuzzy granulation method are innovatively proposed to predict carbon prices. This study first converts carbon prices into incremental granulation time series. A time-varying core line is added to produce nonlinear trend granulation on the foundation of linear trend granulation. The nonlinear trend and residual information are then predicted using the DeeAR network, respectively, and the final prediction result is obtained by adding the predicted values for each. Moreover, a new evaluation index, the comprehensive evaluation of RMSE, MAE, and MAPE as three indicators, is proposed to consider the accuracy of the evaluation index more comprehensively and reliably. The results show that the prediction method has the smallest error in long-term prediction compared with other models. The daily closing price datasets of carbon exchanges published in Shenzhen and Beijing are used to validate the efficacy of this methodology.

Multiscale Fuzzy Entropy-Based Feature Selection

In practice, it is common that there will be the same decision results under different scale conditions. Therefore, knowledge representation based on a single scale feature framework is far from meeting the needs of practical applications. Based on this, multi-scale data has received extensive attention. Feature selection is an important application of fuzzy multigranularity data analysis model. The existing multi-scale fuzzy granulation-based feature selection methods remove redundant or irrelevant features by selecting the optimal scale. However, this will lose the information corresponding to the remaining scale fuzzy granules, which will affect the classification results or learning tasks. Inspired by this, multi-scale fuzzy entropy is defined to fuse the granule information at different scales, and applied to feature selection. First, the feature with maximum multi-scale fuzzy mutual information is first selected. Then, the most significant features are gradually selected by evaluation metric that simultaneously considers the redundancy, relevance and complementary. A multi-scale fuzzy entropy-based feature selection (MFEFS) algorithm by means of this evaluation index is further designed. Finally, the proposed method is compared with some state-of-the-art methods. The experimental results show that the proposed algorithm has higher reduction efficiency than the comparison algorithms.

Hybrid Machine Learning Approach for Evapotranspiration Estimation of Fruit Tree in Agricultural Cyber-Physical Systems.

The flourish of the Internet of Things (IoT) and data-driven techniques provide new ideas for enhancing agricultural production, where evapotranspiration estimation is a crucial issue in crop irrigation systems. However, tremendous and unsynchronized data from agricultural cyber-physical systems bring large computational costs as well as complicate performing conventional machine learning methods. To precisely estimate evapotranspiration with acceptable computational costs under the background of IoT, we combine time granulation computing techniques and gradient boosting decision tree (GBDT) with Bayesian optimization (BO) to propose a hybrid machine learning approach. In the combination, a fuzzy granulation method and a time calibration technique are introduced to break voluminous and unsynchronized data into small-scale and synchronized granules with high representativeness. Subsequently, GBDT is implemented to predict evapotranspiration, and BO is utilized to find the optimal hyperparameter values from the reduced granules. IoT data from Xi'an Fruit Technology Promotion Center in Shaanxi Province, China, verify that the proposed granular-GBDT-BO is effective for cherry tree evapotranspiration estimation with reduced computational time, and acceptable and robust predictive accuracy. Consequently, the precise estimation of crop evapotranspiration could provide operational guidance for plant irrigation, plant conservations, and pest control in the agricultural greenhouse.

Prediction and analysis of time series data based on granular computing.

The advent of the Big Data era and the rapid development of the Internet of Things have led to a dramatic increase in the amount of data from various time series. How to classify, correlation rule mining and prediction of these large-sample time series data has a crucial role. However, due to the characteristics of high dimensionality, large data volume and transmission lag of sensor data, large sample time series data are affected by multiple factors and have complex characteristics such as multi-scale, non-linearity and burstiness. Traditional time series prediction methods are no longer applicable to the study of large sample time series data. Granular computing has unique advantages in dealing with continuous and complex data, and can compensate for the limitations of traditional support vector machines in dealing with large sample data. Therefore, this paper proposes to combine granular computing theory with support vector machines to achieve large-sample time series data prediction. Firstly, the definition of time series is analyzed, and the basic principles of traditional time series forecasting methods and granular computing are investigated. Secondly, in terms of predicting the trend of data changes, it is proposed to apply the fuzzy granulation algorithm to first convert the sample data into coarser granules. Then, it is combined with a support vector machine to predict the range of change of continuous time series data over a period of time. The results of the simulation experiments show that the proposed model is able to make accurate predictions of the range of data changes in future time periods. Compared with other prediction models, the proposed model reduces the complexity of the samples and improves the prediction accuracy.

Fuzzy granular anomaly detection using Markov random walk

Fuzzy information granulation is an important mathematical model in the theory of granular computing that can effectively handle fuzzy or uncertain information. To address the deficiencies of existing anomaly detection techniques that are mainly suitable for certainty data, this study proposes an anomaly detection method based on fuzzy granules. This method uses the fuzzy information granulation model as a unified framework to gradually develop a fuzzy granular anomaly detection method for calculating the anomaly score of each sample. First, the fuzzy granular distance is defined by fusing single-attribute fuzzy granules to represent the dissimilarity between two samples. Second, a matrix is constructed using the fuzzy granular distance between the samples as the state transition matrix of the Markov random walk. Anomalies in the dataset are then detected using the stationary distribution generated by iterative calculations. Finally, the fuzzy granular anomaly score for each object is obtained by normalizing the stationary distribution. Experiments are conducted on public datasets to compare the proposed method with some state-of-the-art anomaly detection methods. The results indicate that the proposed method is effective. The code is publicly available online at https://github.com/BElloney/FGAS.

Short-term load forecasting system based on sliding fuzzy granulation and equilibrium optimizer.

Short-term electricity load forecasting is critical and challenging for scheduling operations and production planning in modern power management systems due to stochastic characteristics of electricity load data. Current forecasting models mainly focus on adapting to various load data to improve the accuracy of the forecasting. However, these models ignore the noise and nonstationarity of the load data, resulting in forecasting uncertainty. To address this issue, a short-term load forecasting system is proposed by combining a modified information processing technique, an advanced meta-heuristics algorithm and deep neural networks. The information processing technique utilizes a sliding fuzzy granulation method to remove noise and obtain uncertainty information from load data. Deep neural networks can capture the nonlinear characteristics of load data to obtain forecasting performance gains due to the powerful mapping capability. A novel meta-heuristics algorithm is used to optimize the weighting coefficients to reduce the contingency and improve the stability of the forecasting. Both point forecasting and interval forecasting are utilized for comprehensive forecasting evaluation of future electricity load. Several experiments demonstrate the superiority, effectiveness and stability of the proposed system by comprehensively considering multiple evaluation metrics.

Instance and Feature Selection Using Fuzzy Rough Sets: A Bi-Selection Approach for Data Reduction

Data reduction, aiming to reduce the original data by selecting the most representative information, is an important technique of preprocessing data. At present, large-scale or huge data are very common and the development of data reduction techniques for such data has attracted much attention. As a powerful tool for handling uncertainty in real-valued data, the fuzzy rough set theory has been widely applied to data reduction including extensive feature selection methods and some instance selection approaches. Nevertheless, not much work has been devoted to the simultaneous selection of feature and instance based on fuzzy rough sets. In this paper, we investigate the fuzzy rough set-based bi-selection issue for data reduction. Specifically, the unified concepts of the importance degrees of fuzzy granules are presented to select the representative instances first and then the critical features. An instance selection algorithm with a noise elimination technique is provided to firstly remove the noise and then select the representative instances according to the importance degrees of fuzzy granules. Then, the importance-degree-preserved attribute reduction is proposed, and a corresponding feature selection algorithm with a wrapper technique is given to search for a best feature subset. Lastly, the bi-selection method based on fuzzy rough sets (BSFRS) is presented for data reduction by integrating the instance selection and the feature selection methods. Moreover, some numerical experiments are conducted to assess the performance of BSFRS, and the results show that BSFRS performs well in terms of the effectiveness.

Set-based integer-coded fuzzy granular evolutionary algorithms for high-dimensional feature selection

Feature selection plays a pivotal role in handling today’s high-dimensional databases by keeping only the most valuable features, leading to less computation, improved performance, and higher transparency in decision-making processes. Despite the considerable advances in combinatorial optimization, this data-preprocessing step is computationally NP-hard and continues to pose critical challenges, particularly for very high-dimensional (VHD) databases. Here, we propose integer coding and fuzzy granulation (FG) as an integral part of evolutionary wrapper-based feature selection. Based on this integer coding, we further propose crossover and mutation operators that employ set operations such as ‘union,’ ‘intersection,’ and ‘complement’ for higher transparency in their evolutionary explorative and exploitative search processes. In addition to its common use as a surrogate technique to avoid unnecessary computations by recognizing similarities, the fuzzy granulation concept also operates as a repulsive strategy that searches for dissimilarities in the elitist and population initialization routines to reach higher population diversity. An ablation study is implemented to discover the role of individual components of this multi-prong approach. The results are then compared on 22 benchmark problems, ranging from 64 to 138672 attributes, with nine competing methods. Superior performance is shown for the proposed approach in terms of accuracy (in 15 of 22 cases) and achieving a substantially smaller (as much as six times less) feature set with considerably less computational cost (by an average of 30 percent), particularly for VHD feature selection

Feature Subset Selection With Multi-Scale Fuzzy Granulation

As a typical multigranularity data analysis model, multi-scale rough sets have attracted considerable attention in recent years. However, classical multi-scale rough sets and most of its extended models can only deal with discrete data, which limits its popularization and application. To overcome this problem, we investigate the fuzzy generalization of multi-scale rough sets as well as their application in feature selection for continuous data. To this end, a new type of decision systems, i.e., multi-scale fuzzy decision systems, is formalized to represent knowledge at different scales. Scaled fuzzy granules in terms of a family of scaled fuzzy relations are introduced, using which the granular structures of fuzzy lower and upper approximations are presented. A heuristic lattice-based optimal scale selection algorithm is then put forward from the viewpoint of maintaining the consistency of decision systems. Decision rules with strong generalization ability can be obtained by selecting appropriate scales. Finally, a forward feature selection algorithm was developed by means of the optimal scale to reduce redundant fuzzy relations. Extensive numerical experiments are further conducted to compare the proposed algorithm with some state-of-the-art algorithms. The experimental results show that our model can improve the generalization ability of fuzzy rough set, so as to be more feasible and effective.

Driver-Centric Velocity Prediction With Multidimensional Fuzzy Granulation

Dear Editor, This letter deals with a real-world problem regarding chaotic time series prediction, where a driver-centric velocity prediction model is presented for vehicle intelligent control and advanced driver assistance, i.e., multi-dimension fuzzy predictor. Inspired by fuzzy granulation technology, a finite-state Markov chain (MC) is reinforced to capture probabilities of the transitions between velocity and acceleration and present signals that vary in a continuous range. The predictability of the multi-dimensional fuzzy predictor is examined by comparing two existing MC-based predictors over the two laboratory cycles and one virtual driving cycle, both of which have high accuracy.

Adaptive Granulation-Based Convolutional Neural Networks With Single Pass Learning for Remote Sensing Image Classification

Convolutional neural networks (CNNs) with the characteristics like spatial filtering, feed-forward mechanism, and back propagation-based learning are being widely used recently for remote sensing (RS) image classification. The fixed architecture of CNN with a large number of network parameters is managed by learning through a number of iterations, and, thereby increasing the computational burden. To deal with this issue, an adaptive granulation-based CNN (AGCNN) model is proposed in the present study. AGCNN works in the framework of fuzzy set theoretic data granulation and adaptive learning by upgrading the network architecture to accommodate the information of new samples, and avoids iterative training, unlike conventional CNN. Here, granulation is done both on the 2-D input image and its 1-D representative feature vector output, as obtained after a series of convolution and pooling layers. While the class-dependent fuzzy granulation on input image space exploits more domain knowledge for uncertainty modeling, rough set theoretic reducts computed on them select only the relevant features for input to CNN. During classification of unknown patterns, a new principle of roughness-minimization with weighted membership is adopted on overlapping granules to deal with the ambiguous cases. All these together improve the classification accuracy of AGCNN, while reducing the computational time significantly. The superiority of AGCNN over some state-of-the-art models in terms of different performance metrics is demonstrated for hyperspectral and multispectral images both quantitatively and visually.