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Time series have yielded impressive results in numerical prediction, yet the presence of noise can significantly affect accuracy. Although interval prediction can minimize noise interference, most methods only predict upper and lower limits separately, resulting in uninterpretable predictions. In this paper, we propose a novel modeling approach for time-series interval prediction that integrates granular computing and fuzzy cognitive maps (FCMs). Granular computing transforms traditional numerical time series into interval time series. Rather than predicting interval values independently, our method mines the fuzzy relationship between information granules to obtain the affiliation matrix. During the prediction stage, an FCM-based model is established to predict the affiliation matrix. We conducted experiments on six publicly available datasets, and results demonstrate that our method reduces the impact of noise while offering improved interpretability for prediction outcomes. More importantly, our approach yields significantly lower interval prediction errors when compared to other advanced methods. [ABSTRACT FROM AUTHOR]

The theory of interval-valued formal contexts was originally derived from fuzzy formal contexts. While the fuzzy formal context can extract information from fuzzy formal contexts more precisely, it lacks theoretical analysis of formal contexts with interval-valued data types. This paper incorporates the three-way concept into interval-valued formal contexts, and partitions the interval value range of objects and attributes into three regions utilizing the notion of three-way decisions. On the basis of interval-valued information granules, the concepts of negative operators and interval-valued three-way concepts are proposed. They can conduct profounder knowledge discovery in interval-valued formal contexts, and a generation algorithm of interval-valued three-way concepts is devised. Finally, the effectiveness of the algorithm is substantiated through experimentation [ABSTRACT FROM AUTHOR]

Multi-granularity rough sets facilitate knowledge-based granular computing, and their compromised models (called CMGRSs) outperform classical optimistic and pessimistic models with extremity. Three-level CMGRSs with statistic-optimization-location effectively process hierarchical granularities with attribute enlargements, and they are worth generalizing for general granularities with arbitrary feature subsets. Thus, three-level CMGRSs on knowledge, approximation, and accuracy are established for arbitrary granularities by using three-way decision (3WD). Corresponding 3WD-CMGRSs adopt statistic-optimization-3WD by adding optimistic and pessimistic bounds to the representative location, so they resort to optimal index sets to acquire the multi-granularity equilibrium and decision systematicness. As a result, multiple CMGRSs emerge within the three-level and three-way framework, they improve the classical MGRSs and enrich 3WD as well as three-level analysis, and exhibit the good simulation, extension, effectiveness, improvement, and generalization. Firstly at the knowledge level, cardinality statistic-optimization improves previous label statistic-optimization for equilibrium realization, so CMGRSs are improved for hierarchical granularities while 3WD-CMGRSs are proposed for arbitrary granularities. Then at the approximation and accuracy levels, measure statistic-optimization determines optimal index sets, so 3WD-CMGRSs are similarly proposed to complete the simulation and extension. Furthermore, mathematical properties and computational algorithms of relevant models are investigated. Finally, three-level 3WD-CMGRSs are illustrated by table examples and are validated by data experiments. [ABSTRACT FROM AUTHOR]

Neighborhood granulation is a classical granulation method. Although it is adequate for clustering and classification tasks, its granules are more complex, and the data representation is binary. This paper proposes a new granulation method based on the neighborhood granulation. Firstly, a detailed definition of the granular form is given with fuzzy rough set theory. Then, a modified fuzzy rough discriminant function is proposed based on neighborhood systems. The samples are globally granulated on single features to construct granules and on multiple features to construct granular vectors. Also, a feature selection technique based on the Chi-square, which strikingly reduces the complexity of the fuzzy rough granular vectors, is introduced to address the disadvantage of the fuzzy rough granular vectors. An ensemble model structure is also proposed in the paper for the mixed nature of fuzzy rough granular vectors. The paper makes a detailed comparison between the fuzzy rough granulation and the neighborhood granulation. The results show that fuzzy rough granulation has higher computational efficiency and classification performance. Finally, a detailed comparison is made between the fuzzy rough granular ensemble model and various classical ensemble algorithms. The final results show that the fuzzy rough granular ensemble model has better robustness and generalization. [ABSTRACT FROM AUTHOR]

Concise granule descriptions for describable granules and approaching description methods for indescribable granules are fundamental issues in granular computing. The concept with only common attributes has been frequently investigated. To explore the granules with some special needs, we propose a new type of compound concepts in this paper: common-and-possible concept. Based on the definitions of concept-forming operations, the logical representations are derived for each of the following types of concepts: formal concept, property oriented concept, possible three-way concept, common-and-possible concept. Furthermore, by utilizing the logical relationship among various concepts, we have derived concise and unified equivalent conditions for describable granules and approaching description methods for indescribable granules for all four kinds of concepts. [ABSTRACT FROM AUTHOR]

We analyze the properties and characteristics of the information structure in incomplete lattice-valued information system (ILIS), we redefine the information structure and the dependence and information distance between the two information structures. In addition, in order to evaluate the uncertainty of ILIS, the concepts of granular measure and entropy measure are expounded, including information granulation, information quantity, rough entropy and information entropy. Finally, we carry out numerical experiments to verify the feasibility of the method, and carry out effective statistical analysis. These results are conducive to the establishment of granular computing framework in ILIS. [ABSTRACT FROM AUTHOR]

Network data is ubiquitous, such as telecommunication, transport systems, online social networks, protein-protein interactions, etc. Since the huge scale and the complexity of network data, former machine learning system tried to understand network data arduously. On the other hand, thought of multi-granular cognitive computation simulates the problem-solving process of human brains. It simplifies the complex problems and solves problems from the easier to harder. Therefore, the application of multi-granularity problem-solving ideas or methods to deal with network data mining is increasingly adopted by researchers either intentionally or unintentionally. This paper looks into the domain of network representation learning (NRL). It systematically combs the research work in this field in recent years. In this paper, it is discovered that in dealing with the complexity of the network and pursuing the efficiency of computing resources, the multi-granularity solution becomes an excellent path that is hard to go around. Although there are several papers about survey of NRL, to our best knowledge, we are the first to survey the NRL from the perspective of multi-granular computing. This paper proposes the challenges that NRL meets. Furthermore, the feasibility of solving the challenges of NRL with multi-granular computing methodologies is analyzed and discussed. Some potential key scientific problems are sorted out and prospected in applying multi-granular computing for NRL research. [ABSTRACT FROM AUTHOR]

Clustering is the main task of machine learning, and is also the core work of granular computing, namely information granulation. At present, most of granular computing based clustering algorithms only utilize the granule features without taking the granule structure into account, especially in the information field where algebraic structure is widely used. From the perspective of granular computing, this paper proposes a clustering method based on algebraic granularity (CMAG). Firstly, the algebraic granularity is newly formulated with the granule structure of an algebraic binary operator. Secondly, the CMAG is proposed with granules of incorporating congruence partition and granule structure of homeomorphic projection. Finally, the CMAG is experimentally compared with the tolerance domain model and the quotient space model, and the results show that the CMAG has better structural completeness and practical robustness. The CMAG can enrich and extend the granular computing theory from granule structure, and will provide a theoretical basis for the combination of granular computing methods and machine learning theory. [ABSTRACT FROM AUTHOR]

The pursuit of environmental sustainability, energy conservation, and emissions reduction has become a global focal point. Electricity is the primary source of energy in our daily lives. Through the analysis of smart power systems, we can efficiently and sustainably harness electrical energy. However, electric power system data inherently contain a wealth of sensitive user information. Therefore, our primary concern is protecting these sensitive user data while performing precise and effective analysis. To address this issue, we have innovatively proposed three granular information models based on differential privacy. In consideration of the characteristics of enterprise electricity consumption data and the imperative need for privacy protection, we implement a reasonable modeling process through data processing, information granulation expression, and the optimization analysis of information granularity. Our datasets encompass enterprise electricity consumption data and related attributes from Hitachi Building Technology (Guangzhou) Co., Ltd's cloud computing center. Simultaneously, we have conducted experiments using publicly available datasets to underscore the model's versatility. Our experimental results affirm that granular computation can improve the utility of differential privacy in safeguarding data privacy. [ABSTRACT FROM AUTHOR]

The proposed research aims to enhance the capabilities of information fusion-based object tracking using thermal and visible imaging. An essential motivation behind this technique is to carve out a framework that may utilize many attributes from several sensors. The built-in particle filter is adapted with the granular computing concept for weighing the particles. Furthermore, the algorithm is extended to obtain source-level fusion after the attribute weight adaptation. After comparing with the state-of-the-art methods, the results obtained suggest that it outperforms the compared trackers from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Pawlak's rough set theory from a categorical point of view, by introducing specific categories of lower and upper operators in order to analyze in a generalized setting the usual approximant operators of rough set theory. We determine several embeddings and isomorphisms between these categories and suitable categories of finitary matroids, set partitions and equivalence relations, some of which already investigated in recent papers. Using the aforementioned isomorphic categories, we exhibit several categorical properties of lower and upper operators. In addition, as one of the main applications of rough set theory concerns Pawlak's information systems and Granular Computing, in the last part of the paper we translate in categorical terms the occurrence of rough sets in Granular Computing and, to this end, we need to work with a category PR of pairings (i.e. generalizations of Pawlak's information systems) and pairing homomorphisms. More specifically, we exhibit several categorical properties of pairings, such as balancedness, completeness, exactness, (RegEpi,Mono-Source)-factorizability and prove that PR is Heyting but, in general, it does not admit coproducts. [ABSTRACT FROM AUTHOR]

Outlier detection is an important topic in data mining. An information system (IS) is a database that shows relationships between objects and attributes. A real-valued information system (RVIS) is an IS whose information values are real numbers. People often encounter missing values during data processing. A RVIS with the miss values is an incomplete real-valued information system (IRVIS). Due to the presence of the missing values, the distance between two information values is difficult to determine, so the existing outlier detection rarely considered an IS with the miss values. This paper investigates outlier detection for an IRVIS via rough set theory and granular computing. Firstly, the distance between two information values on each attribute of an IRVIS is introduced, and the parameter λ to control the distance is given. Then, the tolerance relation on the object set is defined according to the distance, and the tolerance class is obtained, which is regarded as an information granule. After then, λ-lower and λ-upper approximations in an IRVIS are put forward. Next, the outlier factor of every object in an IRVIS is presented. Finally, outlier detection method for IRVIS via rough set theory and granular computing is proposed, and the corresponding algorithms is designed. Through the experiments, the proposed method is compared with other methods. The experimental results show that the designed algorithm is more effective than some existing algorithms in an IRVIS. It is worth mentioning that for comprehensive comparison, ROC curve and AUC value are used to illustrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Fuzzy information granulation theory is based on the way humans granulate and reason about information, and it is essential to the remarkable ability of people to act logically in ambiguous and uncertain situations. In the study of fuzzy information granulation, instead of discussing single fuzzy granules, it is common to consider a fuzzy granular structure arising from a set of fuzzy information granules. Different approaches and perspectives may generate different fuzzy granular structures in the same universe by dividing the object into a number of meaningful fuzzy information granules. However, a specific task usually requires only a selection of representative fuzzy granular structures. Therefore, the main aim of this paper is to group fuzzy granular structures efficiently and accurately. To this end, we first introduce the distances between two fuzzy granular structures and illustrate the relevant properties. Subsequently, k-means and fuzzy c-means clustering algorithms are designed for clustering fuzzy granular structures, and their convergence is demonstrated. In this way, similar fuzzy granular structures can be grouped into the same class. In addition, two evaluation indicators, dispersion and separation, are constructed to evaluate the effect of clustering fuzzy granular structures. Experiments on 12 publicly available datasets demonstrate the feasibility and effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Fuzzy rough set theory has been successfully applied to many attribute reduction methods, in which the lower approximation set plays a pivotal role. However, the definition of lower approximation used has ignored the information conveyed by the upper approximation and the boundary region. This oversight has resulted in an unreasonable relation representation of the target set. Despite the fact that scholars have proposed numerous enhancements to rough set models, such as the variable precision model, none have successfully resolved the issues inherent in the classical models. To address this limitation, this paper proposes an unsupervised attribute reduction algorithm for mixed data based on an improved optimal approximation set. Firstly, the theory of an improved optimal approximation set and its associated algorithm are proposed. Subsequently, we extend the classical theory of optimal approximation sets to fuzzy rough set theory, leading to the development of a fuzzy improved approximation set method. Finally, building on the proposed theory, we introduce a novel, fuzzy optimal approximation-set-based unsupervised attribute reduction algorithm (FOUAR). Comparative experiments conducted with all the proposed algorithms indicate the efficacy of FOUAR in selecting fewer attributes while maintaining and improving the performance of the machine learning algorithm. Furthermore, they highlight the advantage of the improved optimal approximation set algorithm, which offers higher similarity to the target set and provides a more concise expression. [ABSTRACT FROM AUTHOR]

Purpose: The authors test the granularity hypothesis to international inflation spillovers using annual exports and inflation data for 138 countries from 1991 to 2020. This study aims to discuss the aforementioned objective. Design/methodology/approach: First, the authors quantify the power law for the right tail of the export volumes distribution and discuss its implications. Then, the authors compute the granular residual, a measure of shocks to the largest countries. Findings: The authors find export volumes across countries are not Gaussian-distributed but follow a power law. This finding means the largest countries disproportionately impact world inflation. In addition, the authors find that countries with higher relative weight in international trade determine a portion of international spillovers greater than their trade share. Moreover, eight big grains are responsible for the bulk of inflation spillovers. Practical implications: The policy implication is that other countries' central banks should closely monitor the eight big grains when conducting their domestic monetary policy. Originality/value: This is the first study spotting the problem of granular inflation spillovers. [ABSTRACT FROM AUTHOR]

Uncertainty measures are instrumental in describing the classification abilities in information systems, and uncertain information has been measured and processed with granular computing theory. While the fuzzy set-valued information system is a generalization of fuzzy information systems, the relationship between the information granulation and the uncertainty in fuzzy set-valued information systems remains to be studied. This paper probes into uncertainty measures in fuzzy set-valued information systems based on the fuzzy β -neighborhood and the idea of granulation. Specifically, the fuzzy β -neighborhood similarity relation that reflects the similarity between two objects is defined in terms of the nearness degree. We propose the concepts of information granules and granular structures induced by fuzzy β -neighborhood similarity relations, based on which we introduce the granularity measures and rough approximation measures of granular structures in fuzzy set-valued information systems. Given the situation of decision information systems, we propose the granularity-based rough approximation measures by combining granularity measures with rough approximation measures. Experiment results and effectiveness analysis show that the measures we proposed are reasonable and feasible. [ABSTRACT FROM AUTHOR]

Neighborhood systems have been investigated extensively because of their applicability in granular computing. The consistent functions have been used to compare the structures of neighborhood systems. This paper is devoted to a further study of consistent functions and reductions of fuzzy neighborhood systems. Based on some equivalence relations on the universe, we propose a general method for constructing consistent functions. Some equivalent conditions for a function to be consistent are examined. In addition, the discernibility function of fuzzy neighborhood information systems is constructed which is used to compute all reductions of fuzzy neighborhood information systems. Accordingly, we make an analysis of fuzzy neighborhood systems based on three-way classification by using reductions. [ABSTRACT FROM AUTHOR]

In literature granular computing and formal concept analysis algorithm use only single-value attributes to knowledge discovery for the data of spatio-temporal aspects. However, most of the datasets like forest fires and tornado storms involve multiscale values for attributes. The limitation of single-value attributes of the existing approaches indicates only the data related to event occurrence which may be missing the elicitation of important knowledge related to severity of event occurrence. Motivated by these limitations, this research article proposes a novel and generalized method which uses ordinal semantic weighted multiscale values for attributes in formal concept analysis with granular computing measures especially when spatio-temporal attributes are not given. The originality of proposed methodology is using ordinal semantic weighted multiscale values for attributes that give complete information of event occurrences. Moreover, the use of ordinal semantic weighted multiscale values improves the results of granular computing measures. The significance of proposed approach is well explained by experimental evaluation performed on publicly available datasets on storm occurring in different States of America. [ABSTRACT FROM AUTHOR]

Unsupervised anomaly detection is an important research direction in the process of unsupervised knowledge acquisition. It has been successfully applied in many fields, such as online fraud identification, loan approval, and medical diagnosis. Multi-granularity thinking is an effective information fusion method for solving problems in a multi-granular environment, which allows people to understand and analyze problems from multiple perspectives. However, there are few studies on building anomaly detection models using the idea of multi-fuzzy granules. To this end, this paper constructs a multi-fuzzy granules anomaly detection method by using a fuzzy rough computing model. In this method, a hybrid metric is first used to calculate the fuzzy relations. Then, two ranking sequences are constructed based on the significance of attributes. Furthermore, forward and reverse multi-fuzzy granules are constructed to define anomaly scores based on the ranking sequences. Finally, a multi-fuzzy granules-based anomaly detection algorithm is designed to detect anomalies. The experimental results compared with existing algorithms show the effectiveness of the proposed algorithm. • Hybrid metric is adopted to compute the fuzzy similarity relation. • Multi-fuzzy granules are introduced for the first time to construct detection model. • Multi-Fuzzy Granules Anomaly Detection (MFGAD) algorithm is designed. • Experimental results demonstrate that MFGAD is effective. [ABSTRACT FROM AUTHOR]

Via Granular Computing (GrC), one can create effective computational frameworks for obtaining information from data, motivated by the human perception of combining similar objects. Combining knowledge gained via GrC with a Fuzzy inference engine (Neural‐Fuzzy) enable us to develop a transparent system. While weighting variables based on their importance during the iterative data granulation process has been proposed before (W‐GrC), there is no work in the literature to demonstrate effectiveness and impact on Type‐2 Fuzzy Logic systems (T2‐FLS). The main contribution of this paper is to extend W‐GrC, for the first time, to both Type‐1 and Type‐2 models known as Radial Basis Function Neural Network (RBFNN) and General Type‐2 Radial Basis Function Neural Network (GT2‐RBFNN). The proposed framework is validated using popular datasets: Iris, Wine, Breast Cancer, Heart and Cardiotocography. Results show that with the appropriate selection of feature weight parameter, the new computational framework achieves better classification accuracy outcomes. In addition, we also introduce in this research work an investigation on the modelling structure's interpretability (via Nauck's index) where it is shown that a good balance of interpretability and accuracy can be maintained. [ABSTRACT FROM AUTHOR]

Partial label learning refers to the issue that each training sample corresponds to a candidate label set containing only one valid label. Feature selection can be viewed as an effective pre-processing technology to improve the generalization performance of learning models, while the partial label feature selection task is challenging due to ambiguous labeling information. To this end, this paper utilizes granular ball computing and neighborhood rough sets to put forward a disambiguation-based partial label feature selection algorithm via feature dependency and label consistency. Firstly, the proposed algorithm performs an adaptive neighbor aggregation based on granular balls to disambiguate candidate labels. Adaptive neighbors are flexible to make more efficient learning performance. Then, considering the labeling confidence induced by disambiguation, the significance of each feature is evaluated by fusing the feature dependency from the neighborhood granularity and the label consistency among the nearest neighbors. Neighborhood rough sets directly handle continuous features that can reduce the adverse impact of data discretization on feature selection. The label consistency among adjacent samples is important for measuring feature discrimination. The fusion of feature dependency and label consistency can facilitate performance improvement. Finally, experiments conducted on eight controlled UCI and five real-world partial label datasets demonstrate that the proposed algorithm can improve the generalization performance of partial label learning and achieve superior performance compared to the partial label feature selection methods. • A novel disambiguation-based partial label feature selection method is proposed. • Fusion strategy of feature dependency and label consistency is considered. • Granular-ball based adaptive neighbors are utilized to disambiguate candidate labels. • Neighborhood granularity is used to evaluate dependency degree of the features. • Extensive experiments show that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

This article proposes a new methodology of unsupervised event prediction from videos. Detecting events from videos without prior information is a challenging task, as there are no well-accepted definitions about events in a video. It is commonly known that the presence of moving elements in a video scene could be considered as part of an event. The possibility of an event occurring becomes higher if there is an abrupt change in the motion patterns of different object(s) present in that video scene. In this paper, we defined a method to model this phenomenon of object motion. Since we have not considered any prior information while modeling it, the initial event and nonevent classification is carried out with rough set-based approximations, namely positive, boundary, and negative, in the incomplete knowledge base, resulting in an event-nonevent rough sets. We generate three regions with rough sets. Negative class labels are assigned for static objects and those moving with predictable paths. The objects with a huge change in motion are labeled to be positive events. The remaining objects are kept in the boundary region. However, if there is a gradual change in the motion pattern, there arises some possibility of an event occurring. To define the terms, like possible events and must be event, we have fuzzified the boundary region of event-nonevent rough set and assigned different degrees of possibility of an event to occur if there is a change in motion patterns in the trajectory of the objects. That is, the event, nonevent regions are classified with rough sets, and the boundary region is fuzzified with fuzzy sets. We have validated this newly defined event-nonevent rough-fuzzy sets with experimental demonstrations where the proposed method successfully predicted the events to occur in video sequences. [ABSTRACT FROM AUTHOR]

The random forest is a combined classification method belonging to ensemble learning. The random forest is also an important machine learning algorithm. The random forest is universally applicable to most data sets. However, the random forest is difficult to deal with uncertain data, resulting in poor classification results. To overcome these shortcomings, a broad granular random forest algorithm is proposed by studying the theory of granular computing and the idea of breadth. First, we granulate the breadth of the relationship between the features of the data sets samples and then form a broad granular vector. In addition, the operation rules of the granular vector are defined, and the granular decision tree model is proposed. Finally, the multiple granular decision tree voting method is adopted to obtain the result of the granular random forest. Some experiments are carried out on several UCI data sets, and the results show that the classification performance of the broad granular random forest algorithm is better than that of the traditional random forest algorithm. [ABSTRACT FROM AUTHOR]

Intrusion detection systems have become one of the important tools for network security due to the frequent attacks brought about by the explosive growth of network traffic. Autoencoder is an unsupervised learning model with a neural network structure. It has a powerful feature learning capability and is effective in intrusion detection. However, its network construction suffers from overfitting and gradient disappearance problems. Traditional granular computing methods have advantages in solving such problems, but the process is relatively complex, the granularity dimension is high, and the computational cost is large, which is not suitable for application in intrusion detection systems. To address these problems, we propose a novel autoencoder: Granular AutoEncoders (GAE). The granulation reference set is constructed by random sampling. The granulation of training samples is based on single-feature similarity in a reference set to form granules. The granulation of multiple features results in granular vectors. Some operations of granules are defined. Furthermore, we propose some granular measures, including granular norms and granular loss functions. The GAE is further applied to the field of intrusion detection by designing an anomaly detection algorithm based on the GAE. The algorithm determines whether the network flows are anomalous by comparing the difference between an input granular vector and its output granular vector that is reconstructed by the GAE. Finally, some experiments are conducted using an intrusion detection dataset, comparing multiple metrics in terms of precision, recall, and F1-Score. The experimental results validate the correctness and effectiveness of the intrusion detection method based on GAE. And contrast experiments show that the proposed method has stronger ability for detecting anomalies than the correlation algorithms. [ABSTRACT FROM AUTHOR]

Industrial dynamic complex event recognition (CER) can provide decision makers with reference for fault diagnosis and process optimization. It is one of the key steps to ensure the successful completion of each step of industrial production. How to make interpretable reasoning and recognition under incomplete data is a very challenging problem. Our hypothesis is to use our FGR-CER framework to identify complex events in the case of data missing. To address the challenges, we propose a new interpretable fuzzy granular reasoning framework for industrial dynamic complex event recognition framework (FGR-CER). In this framework, event calculus and induction logic are introduced to retain the semantic information of the sensor and make the complex events recognition interpretable. FGR-CER uses the idea of fuzzy set to deal with incomplete data. At the same time, in order to reduce the time complexity of the framework, FGR-CER use the idea of granular computing to optimize the reasoning process, making the reasoning process from coarse-grained to fine-grained according to human thinking. Finally, the proposed FGR-CER is evaluated on the synthetic data set and the real data set, which proved that FGR-CER is better than other algorithms in precision, recall and NDCG for interpretable industrial dynamic event recognition with incomplete data. [ABSTRACT FROM AUTHOR]

Outlier detection has been broadly used in industrial practices such as public security and fraud detection, etc. Outlier detection from various perspectives against different backgrounds has been proposed. However, most of outlier detection consider categorical or numerical data. There are few researches on outlier detection for set-valued data, and a set-valued information system (SVIS) is a proper way of tackling the problem of missing values in data sets. This paper investigates outlier detection for set-valued data based on rough set theory (RST) and granular computing (GrC). First, the similarity between two information values in an SVIS is introduced and a variable parameter to control the similarity is given. Then, the tolerance relations on the object set are defined, and based on this tolerance relation, θ-lower and θ-upper approximations in an SVIS are put forward. Next, the outlier factor in an SVIS is presented and applied to various data sets. Finally, outlier detection method for set-valued data based on RST and GrC is proposed, and the corresponding algorithms are designed. Through numerical experiments based on UCI, the designed algorithm is compared with six other detection algorithms. The experimental results show the designed algorithm is arguably the best choice under the context of an SVIS. It is worth mentioning that for a comprehensive comparison, we use two criteria: AUC value and F-1 measure, to show the superiority of the designed algorithm. [ABSTRACT FROM AUTHOR]

Knowledge discovery through spatial and temporal aspects of data related to occurrences of events has many applications in digital forensics. Specifically, in electronic surveillance, it is helpful to construct a timeline to analyze information. The existing techniques only analyze the occurrence and co-occurrence of events; however, in general, there are three aspects of events: occurrences (and co-occurrences), nonoccurrences, and uncertainty of occurrences/non-occurrences with respect to spatial and temporal aspects of data. These three aspects of events have to be considered to better analyze periodicity and predict future events. This study focuses on the spatial and temporal aspects given in intuitionistic fuzzy (IF) datasets using the granular computing (GrC) paradigm; formal concept analysis (FCA) was used to understand the granularity of data. The originality of the proposed approach is to discover the periodicity of events data given in IF sets through FCA and the GrC paradigm that helps to predict future events. An experimental evaluation was also performed to understand the applicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Multi-source information fusion (MSIF) is a useful strategy for combining complimentary data from numerous information sources to produce an overall precise description, which can help with effective decision-making, prediction, and categorization, etc. In order to find the objects that are different from the expected ones after fusion, i.e., anomalies, or outliers, an MSIF model is put forward for outlier detection. This is a two-stage model that includes fusion of multiple information sources and outlier detection of fused data. The first stage uses information sets to construct uncertainty criteria for information source values and combines multiple information sources into a single information source based on the minimum uncertainty strategy. The second stage uses the Gaussian kernel method for possibility modeling based on the fused data to construct knowledge granules. From the perspective of granular computing, outliers in the fused data can be assigned to each knowledge granule. Then, we can find all outliers just by evaluating these knowledge granules. Inspired by this, the fuzzy knowledge measure (FKM) is proposed to evaluate the knowledge granule. Moreover, several metrics are induced on the basis of FKM to describe outliers in knowledge granules and an FKM-based outlier detection algorithm (FKMOD) is designed. Finally, we conduct the experiments on sixteen open access outlier detection datasets. The experimental results show that the proposed FKMOD method has more accurate detection performance than nine classical methods. • A unified multi-source information fusion model is proposed for outlier detection. • Information set is used to deal with uncertainty of information source values. • A novel fuzzy knowledge measure is presented to characterize the outlier factors. • The proposed FKMOD algorithm can efficiently find outliers in fused data. [ABSTRACT FROM AUTHOR]

In this study, we are concerned with a new design methodology of M + 1-way classification mechanism. The intent is to reduce the cost of error prediction caused by insufficient evidence. The study is motivated by the notion of three-way decisions, which has been successfully used in various application areas to build human-centric systems. In contrast to traditional multiple classifications, one additional class is added into the proposed architecture to represent the reject decision made on foreign patterns, which exhibit significant differences compared to the patterns used for constructing the classification models. A collection of information granules is constructed on the basis of available experimental evidence to form a compact and interpretable representation of the feature space occupied by the native patterns. The patterns located outside the regions occupied by these information granules are identified and filtered out prior to classification while only the native patterns are subject to classification. The proposed methodology leads to a human-centric and human-interactive construct in which the rejected patterns need further processing. Different distance functions are utilized in the construction of information granules. The performance of the proposed architecture is evaluated involving one synthetic dataset and a collection of publicly available datasets. [ABSTRACT FROM AUTHOR]

The construction of information granules is a significant and interesting topic of Granular Computing (GrC) in which information granules play a vital role in representing and describing data, and it has become one of the most effective frameworks for solving complex problems. In this study, we are interested in the collaborative impacts of several different characteristics on constructing information granules, and a novel synergistic mechanism of the principle of justifiable granularity is utilized in developing information granules. The synergistic mechanism is finalized with a two-phase process—to start with, the principle of justifiable granularity and Fuzzy C-Means Clustering method are combined to develop a collection of information granules. First, the available experimental data is transformed (normalized) into fuzzy sets following the standard Fuzzy C-Means Clustering method. Then, information granules are developed based on the elements located in different clusters with the use of the principle of justifiable granularity. In the sequel, the positions of information granules are updated by considering the collaborative impacts of the other information granules with the parameters of specifying the level of influence. Experimental studies are conducted to illustrate the nature and feasibility of the proposed framework based on the synthetic data as well as a series of publicly available datasets coming from KEEL machine learning repositories. [ABSTRACT FROM AUTHOR]

Optimal granularity selection is a critical link in constructing multi-granularity features in autoencoder networks. Aiming at the problem of unreasonable granularity selection method in autoencoder networks, which leds to unsatisfactory feature extraction effect, high misclassification cost, and high testing cost, this paper proposed a granularity layer selection strategy based on mini-batch gradient descent (MBGD). This approach reconstructed the multi-granularity space by changing the granularity selection method and designed a new cost-sensitive multi-granularity three-way decision model based on a deep belief network (DBN). The superior granularity selection method enhanced the feature extraction ability of the network, promoted the construction of multi-granularity space to develop towards the fastest reaching the most fine-grained area, and reduced the image reconstruction error to achieve more minor misclassification cost and test cost. The experimental results show that providing a reasonable granularity selection strategy improves the decision accuracy of the cost-sensitive multi-granularity three-way decision model, and can obtain the optimal granular layer with the smallest total cost faster under the given cost. [ABSTRACT FROM AUTHOR]

Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs' psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies. [ABSTRACT FROM AUTHOR]

Forecasting trend and variation ranges for time series has been challenging but crucial in real-world modeling. This study designs a hybrid time series forecasting (FIGDS) model based on granular computing and dynamic selection strategy. Firstly, with the guidance of the principle of justifiable granularity, a collection of interval-based information granules is formed to characterize variation ranges for time series on a specific time domain. After that, the original time series is transformed into granular time series, contributing to dealing with time series at a higher level of abstraction. Secondly, the L1 trend filtering method is applied to extract trend series and residual series. Furthermore, this study develops hybrid predictors of the trend series and residual series for forecasting the variation range of time series. The ARIMA model is utilized in the forecasting task of the residual series. The dynamic selection strategy is employed to identify the ideal forecasting models from the pre-trained multiple predictor system for forecasting the test pattern of the trend series. Eventually, the empirical experiments are carried out on ten time series datasets with a detailed comparison for validating the effectiveness and practicability of the established hybrid time series forecasting method. [ABSTRACT FROM AUTHOR]

Clustering, as one of the main tasks of machine learning, is also the core work of granular computing, namely granulation. Most of the recent granular computing based clustering algorithms only utilize the plain granule features without taking the granule structure into account, especially in information area with widespread application of algebraic structure. This paper aims at proposing an algebraic structure based clustering method from granular computing prospective. Specifically, the algebraic structure based granularity is firstly formulated based on the granule structure of an algebraic binary operator. An algebraic structure based clustering method is then proposed by incorporating congruence partitioning granules and homomorphically projecting granule structure. Finally, proof of the lattice at multiple hierarchical levels and comparative analysis of experimental cases validate the effectiveness of the proposed clustering method. The algebraic structure based clustering method can provide a general framework to perform granularity clustering using the algebraic granule structure information. It meanwhile advances the granular computing methods by combing the granular computing theory and the clustering theory. [ABSTRACT FROM AUTHOR]

The most popular algorithms used in unsupervised learning are clustering algorithms. Clustering algorithms are used to group samples into a number of classes or clusters based on the distances of the given sample features. Therefore, how to define the distance between samples is important for the clustering algorithm. Traditional clustering algorithms are generally based on the Mahalanobis distance and Minkowski distance, which have difficulty dealing with set-based data and uncertain nonlinear data. To solve this problem, we propose the granular vectors relative distance and granular vectors absolute distance based on the neighborhood granule operation. Further, the neighborhood granular meanshift clustering algorithm is also proposed. Finally, the effectiveness of neighborhood granular meanshift clustering is proved from two aspects of internal metrics (Accuracy and Fowlkes–Mallows Index) and external metric (Silhouette Coeffificient) on multiple datasets from UC Irvine Machine Learning Repository (UCI). We find that the granular meanshift clustering algorithm has a better clustering effect than the traditional clustering algorithms, such as Kmeans, Gaussian Mixture and so on. [ABSTRACT FROM AUTHOR]

Rule-based modeling is a useful approach in modeling both complex nonlinear and non-numeric systems, e.g. having linguistic information. However, modeling complex systems in big data era brings new challenges for conventional rule-based modeling, such as high computation overhead and low representation ability of rule. To address these problems, this paper proposed an advanced rule-based modeling method-based DBSCAN-inspired granular descriptors. First, to understand the essential characteristics of data and enhance rules' representation ability, data structures are obtained by DBSCAN clustering algorithm, which has high flexibility at coping with diverse geometry. Second, numerous granular descriptors are constructed in the refined representation of data structures and used for fuzzy rule formation. This granular computing process could effectively reduce computation overhead of big data analysis. Finally, the proposed rule-based model consists of fuzzy rules and interval outputs, which are resulted from structural granular descriptors and justifiable granulating respectively. Experimental studies concerning synthetic data and publicly available data illustrated that the proposed method can achieve prior performance on both modeling and time consuming than conventional rule-based modeling via FCM. Therefore, it is verified the developed approach is feasible and useful to be applied in modeling real complex engineering systems. [ABSTRACT FROM AUTHOR]

In group decision-making problems, experts often form multiple subgroups depending upon their backgrounds or attitudes. To explore the effect of different types of subgroups' formation on the final decision and to make the decision process more conforming to human custom, we propose a comprehensive study on the effect of "multi-subgroup background" on a basis of weights optimization and Granular Computing techniques. Firstly, a comparison of different types of clustering strategies is realized to find the most suitable method for clustering experts. Since Analytical Hierarchy Process is selected as the fundamental model, it becomes a reciprocal matrices' or eigenvectors' clustering task. Secondly, allocation strategies of information granularity to each expert along with weight to each subgroup are carefully designed and optimized. Information granularity is viewed as a design asset to provide experts with some flexibility to adjust their evaluation results, whereas weights reflect the importance degrees of different subgroups and further help to increase the consensus. A granulation-degranulation process is developed to evaluate the performance of a set of weights and granularities under a multi-criteria objective's guidance. Thirdly, a proper evolutionary optimization method like particle swarm optimization is redesigned to iteratively generate the best set of information granularities and weights under an equality constraint condition. A series of numerical studies on synthetic data and real-world data are executed to verify the effectiveness of our method. The results show same trend present across experts. [ABSTRACT FROM AUTHOR]

Information system (IS) is a significant model in the field of artificial intelligence. Information structure is not only a research direction in the field of granular computing (GrC), but also an important method to study an IS. A multiset-valued information system (MVIS) refers to an IS where information values are multisets. A MVIS can be seen as a model that is the result of information fusion of multiple categorical ISs. This model helps deal with missing values in the dataset. This paper studies information structures in a MVIS on the view of GrC and consider their application for uncertainty measurement (UM). First of all, some notions of multisets and probability distribution sets (PDSs) are proposed. Naturally, relationships between multisets and PDSs are researched. Then, the concept of a MVIS based on the notion of multisets is given, and the internal structure of a MVIS is revealed by an incomplete information system (IIS). Furthermore, tolerance relations in a MVIS are defined by using Hellinger distance, and tolerance classes are obtained to construct the information structures of a MVIS. Considering the association of information structures, relationships between information structures are raised from the two aspects of dependence and separation. Moreover, some properties between information structures are provided by using information distance and inclusion degree. Finally, four UMs as the applications of information structures are investigated, and comprehensive experiments on several datasets demonstrate the feasibility and superiority of the proposed measures. These results will be helpful for establishing a framework of GrC in a MVIS and studying UM. [ABSTRACT FROM AUTHOR]

Artificial intelligence is often inspired by biological solutions. Prototypes are among these inspirations. Humans often describe complex entities by comparing them to previously known items (prototypes) instead of providing a detailed description. In this study, we apply this approach to neuro-fuzzy systems. Neuro-fuzzy systems operate using fuzzy IF-THEN rules. In our approach, the premises of rules are represented by prototypes. A new item is compared to the prototypes (as wholes) in the rule premises and its similarities to the prototypes in the rules define the firing strengths of the rules. The similarity is assessed based on the Minkowski metric. Prototypes are elaborated by granulation of the input domain with clustering and by applying the principle of justifiable granularity. We tested the proposed method in numerical experiments based on the regression task for benchmark data sets in public data repositories. [ABSTRACT FROM AUTHOR]