Granular Computing Research Articles

GB-RVFL: Fusion of randomized neural network and granular ball computing

The random vector functional link (RVFL) network is a prominent classification model with strong generalization ability. However, RVFL treats all samples uniformly, ignoring whether they are pure or noisy, and its scalability is limited due to the need for inverting the entire training matrix. To address these issues, we propose granular ball RVFL (GB-RVFL) model, which uses granular balls (GBs) as inputs instead of training samples. This approach enhances scalability by requiring only the inverse of the GB center matrix and improves robustness against noise and outliers through the coarse granularity of GBs. Furthermore, RVFL overlooks the dataset’s geometric structure. To address this, we propose graph embedding GB-RVFL (GE-GB-RVFL) model, which fuses granular computing and graph embedding (GE) to preserve the topological structure of GBs. The proposed GB-RVFL and GE-GB-RVFL models are evaluated on KEEL, UCI, NDC and biomedical datasets, demonstrating superior performance compared to baseline models.

Research on Dynamic Evaluation Method of Tourist Destination Accessibility Based on Interpretive Structure Model

Because of its core role in the process of tourism, tourism destination has always been the focus of discussion among the industry, but the comprehensive evaluation of tourism destination is rarely mentioned. This paper selects tourism destination as the focus of investigation, gives the evaluation method of tourism destination, adapts to the trend of tourism modernization, and discusses the quantifiable model of tourism destination evaluation. This paper first selects several tourism destinations as samples, collects and combs the information related to spatial equity of tourism destinations, and determines the main problem categories of spatial equity of tourism destinations. Then, through the summary of relevant data and case analysis, a framework of tourism target accessibility risk factors is formed. At the same time, considering the interaction between risk factors, we then give a method to determine the weight that can improve granular computing. First, we use this method to obtain the quotient space family with hierarchical characteristics through the similarity relationship between data, and then we can calculate the importance of each feature in the quotient space family, so as to obtain the corresponding weight between different influence indexes. Finally, the paper takes the tourism destination spatial equity problem as the main research goal, and through the dynamic evaluation of the tourism destination spatial equity risk impact structure using the interpretive structure model, and describes the schematic diagram of its impact structure, so as to find out the direct, source, process and other factors that cause the problem.

Granular computing-based time series anomaly pattern detection with semantic interpretation

Time series analysis may suffer from the “curse of dimensionality” due to its high-dimensionality characteristics. In terms of this issue, information granulation offers an effective vehicle to process time series at a higher level of abstraction. To take this advantage, this study conducts an interpretable time series anomaly pattern detection under the framework of granular computing, where each time series is granulated into a series of semantics according to its patterns and the anomaly ones are identified based on the obtained semantics. First, the time series is partitioned into a predefined number of segments and trend-based information granules are formed for the data points in each time interval. Guided by the principle of justifiable granularity, the granular results maintaining the main features of the original time series realize informative feature extraction and meaningful dimensionality reduction. Then, to realize semantic anomaly pattern detection, the Axiomatic Fuzzy Set (AFS) theory is generalized to construct and compute with semantic time series, and an AFS-based anomaly score is proposed to discover anomaly patterns. In the experiments, the proposed method is conducted on both UCR data sets and real-world time series, where the detected anomaly patterns are equipped with well-defined semantics.

Improving patient’s medical history classification using a feature construction approach based on situation awareness and granular computing

AbstractHealthcare decision support systems aid physicians in disease classification by analyzing patients’ medical histories to suggest preliminary diagnoses. As physicians largely base their analysis on anamnesis, integrating this process into an automated recommendation system can expedite decision-making and transition to relevant clinical investigations, thus enhancing efficiency in diagnosing potential pathologies. In this research, an innovative method for feature construction is introduced, drawing on the concepts of Situation Awareness and Granular Computing. The aim of this method is to enhance the performance of out-of-the-box classification algorithms used in machine learning. The approach is specifically tailored to mimic physicians’ cognitive processes when analyzing a patient’s medical history, resulting in the generation of new, information-dense features that can be used for classification tasks. By employing this strategy, a deeper comprehension of the data can be achieved, as well as a more precise categorization of anamneses in relation to possible medical conditions. To authenticate the efficacy of the proposed technique, three major disease categories, namely cardiac, gastrointestinal, and thyroid, were considered. The dataset comprised 1213 medical histories. The experimental results indicate that the study’s six classifiers attained a balanced accuracy exceeding 90%. Among these, the SVM classifier demonstrated the highest balanced accuracy at 93%. Overall, the proposed approach resulted in an average increase of 16 percentage points in balanced accuracy, representing an improvement over the traditional methods commonly employed in machine learning. This approach could be integrated into a clinical decision support system, aiding physicians in accurately identifying necessary investigations and expediting diagnosis.

Seismic vulnerability assessment of buildings using rapid visual screening for hybrid UMNN-RFO approach

This chapter proposes a hybrid approach for seismic vulnerability assessment of buildings using rapid visual screening (RVS). The Unconstrained Monotonic Neural Network (UMNN) and Red Fox Optimisation (RFO) are combined to create the hybrid technique, thus, the term ‘UMNN-RFO approach’. The UMNN algorithm predicts the RVS score and the RFO algorithm optimizes the RVS score. The RVS methods via Google Maps are being used to examine the Andaman and Nicobar Islands because it is one of the main earthquake prone regions in the world. A score was given after a screening that looked at Reinforced Concrete moment-resisting frames, load-bearing structures, steel frames (SF) and wooden frames (WF). By then, the MATLAB platform will have the proposed model implemented. The proposed approach outperforms all current techniques, including Granular Computing Artificial Neural Network (GrC-ANN), Particle Swarm Optimization-Back Propagation Neural Network (PSO-BPNN) and Genetic Algorithm-Artificial Neural Network (GA-ANN). The proposed method’s accuracy is 90%, determination coefficient is 0.91 and the Root Mean Square error is 0.27%. From the result, the proposed method concluded that older structures are more likely to sustain greater damage shortly than more recently built ones based on the score.

Effective Value Analysis of Fuzzy Similarity Relation in HQSS for Efficient Granulation.

Hierarchical quotient space structure (HQSS), as a typical description of granular computing (GrC), focuses on hierarchically granulating fuzzy data and mining hidden knowledge. The key step of constructing HQSS is to transform the fuzzy similarity relation into fuzzy equivalence relation. However, on one hand, the transformation process has high time complexity. On the other hand, it is difficult to mine knowledge directly from fuzzy similarity relation due to its information redundancy, i.e., sparsity of effective information. Therefore, this article mainly focuses on proposing an efficient granulation approach for constructing HQSS by quickly extracting the effective value of fuzzy similarity relation. First, the effective value and effective position of fuzzy similarity relation are defined according to whether they could be retained in fuzzy equivalence relation. Second, the number and composition of effective values are presented to confirm that which elements are effective values. Based on these above theories, redundant information and sparse effective information in fuzzy similarity relation could be completely distinguished. Next, both isomorphism and similarity between two fuzzy similarity relations are researched based on the effective value. The isomorphism between two fuzzy equivalence relations is discussed based on the effective value. Then, the algorithm with low time complexity for extracting effective values of fuzzy similarity relation is introduced. On the basis, the algorithm for constructing HQSS is presented to realize efficient granulation of fuzzy data. The proposed algorithms could accurately extract effective information from the fuzzy similarity relation and construct the same HQSS with the fuzzy equivalence relation while greatly reducing the time complexity. Finally, relevant experiments on 15 UCI datasets, 3 UKB datasets, and 5 image datasets are shown and analyzed to verify the effectiveness and efficiency of the proposed algorithm.

Sequential three-way group decision-making for double hierarchy hesitant fuzzy linguistic term set

Group decision-making (GDM) characterized by complexity and uncertainty is an essential part of various life scenarios. Most existing researches lack tools to fuse information quickly and interpret decision results for partially formed decisions. This limitation is particularly noticeable when there is a need to improve the efficiency of GDM. To address this issue, a novel multi-level sequential three-way decision for group decision-making (S3W-GDM) method is constructed from the perspective of granular computing. This method simultaneously considers the vagueness, hesitation, and variation of GDM problems under double hierarchy hesitant fuzzy linguistic term sets (DHHFLTS) environment. First, for fusing information efficiently, a novel multi-level expert information fusion method is proposed, and the concepts of expert decision table and the extraction/aggregation of decision-leveled information based on the multi-level granularity are defined. Second, the neighborhood theory, outranking relation and regret theory (RT) are utilized to redesign the calculations of conditional probability and relative loss function. Then, the granular structure of DHHFLTS based on the sequential three-way decision (S3WD) is defined to improve the decision-making efficiency, and the decision-making strategy and interpretation of each decision-level are proposed. Furthermore, the algorithm of S3W-GDM is given. Finally, an illustrative example of diagnosis is presented, and the comparative and sensitivity analysis with other methods are performed to verify the efficiency and rationality of the proposed method.

Granular transfer learning

Transfer learning is aimed at supporting the design of machine learning models in the target domain Dt, given that the knowledge (model) has already been constructed in the source domain Ds. The domains Dt and Ds (as well as the corresponding tasks Ts and Tt) are similar, yet not identical. As a result, the model transferred from Ds to Dt in this new environment exhibits its relevance (credibility) only to some limited extent. In this study, we develop an original approach, where we advocate that the knowledge transfer (model transfer) gives rise to a granular model where the level of information granularity associated with the produced results quantifies the relevance (quality or credibility) of the transferred model. In other words, we stress that the quality of knowledge transferred to Dt becomes captured through a granular generalization of the original numeric model. The overall systematic design process is elaborated on by focusing on the development process of granular neural networks carried out on a basis of the numeric neural networks coming from Ds. The key aspect of the design is to elevate the existing numeric neural network to its granular counterpart by admitting that the connections of the developed model come in the form of information granules, in particular intervals and fuzzy sets. The optimization process is guided by adjusting (optimizing) the level of information granularity being regarded as an essential design asset. The optimized performance index builds upon the descriptors of information granules commonly encountered in Granular Computing. In particular, coverage and specificity measures are treated as sound performance indicators of the quality of knowledge transfer (viz. the performance of the granular neural network expressed in the target domain). Several illustrative examples are provided to visualize the performance of the established design environment.

Integration of Control Strategies for Cleaning Based on Granular Computing

Cleaning control based on changes in cleaning loss rate and impurity rate has emerged as a hot topic in the research on intelligent control for rice and wheat combined harvesters. However, numerous operation parameters can lead to deviations beyond the normal range of cleaning loss rate and impurity rate. The impact of cleaning control parameters in rice and wheat combined harvesters on cleaning loss rate and impurity rate often tends to be contradictory. How to combine different contradictory cleaning control strategies to get a more widely used and better cleaning control strategy is a hot issue in the current cleaning control research. In this paper, the granularity of quotient space is introduced into the cleaning control based on operation parameters, and a cleaning control model based on granularity synthesis theory is proposed. This method first constructs a knowledge base for intelligent control of cleaning tailored to the cleaning loss rate and impurity rate using production rule representation, and considers that these control strategies constitute different quotient spaces, and then organizes these quotient spaces according to granularity synthesis theory to get the cleaning control strategy. The experimental results verify that the validity of the cleaning control based on granular computing is better than fuzzy control.

Explainable Histopathology Image Classification with Self-organizing Maps: A Granular Computing Perspective

The automatic analysis of histology images is an open research field where machine learning techniques and neural networks, especially deep architectures, are considered successful tools due to their abilities in image classification. This paper proposes a granular computing methodology for histopathological image classification. It is based on embedding tiles of histopathology images using deep metric learning, where a self-organizing map is adopted to generate the granular structure in this learned embedding space. The SOM enables the implementation of an explainable mechanism by visualizing a knowledge space that the experts can use to analyze and classify the new images. Additionally, it provides confidence in the classification results while highlighting each important image fragment, with the benefit of reducing the number of false negatives. An exemplary case is when an image detail is indicated, with small confidence, as malignant in an image globally classified as benign. Another implemented feature is the proposal of additional labelled image tiles sharing the same characteristics to specify the context of the output decision. The proposed system was tested using three histopathology image datasets, obtaining the accuracy of the state-of-the-art black-box methods based on deep learning neural networks. Differently from the methodologies proposed so far for the same purpose, this paper introduces a novel explainable method for medical image analysis where the advantages of the deep learning neural networks used to build the embedding space for the image tiles are combined with the intrinsic explainability of the granular process obtained using the clustering property of a self-organizing map.

Advancing machine learning for identifying cardiovascular disease via granular computing

<p>Machine learning in cardiovascular disease has broad applications in healthcare, automatically identifying hidden patterns in vast data without human intervention. Early-stage cardiovascular illness can benefit from machine learning models in drug selection. The integration of granular computing, specifically z-numbers, with machine learning algorithms, is suggested for cardiovascular disease identification. Granular computing enables handling unpredictable and imprecise situations, akin to human cognitive abilities. Machine learning algorithms such as Naïve Bayes, K-Nearest Neighbor (KNN), Random Forest, and Gradient Boosting are commonly used in constructing these models. Experimental findings indicate that incorporating granular computing into machine learning models enhances the ability to represent uncertainty and improves accuracy in cardiovascular disease detection.</p>

A Granulation Strategy-Based Algorithm for Computing Strongly Connected Components in Parallel

Granular computing (GrC) is a methodology for reducing the complexity of problem solving and includes two basic aspects: granulation and granular-based computing. Strongly connected components (SCCs) are a significant subgraph structure in digraphs. In this paper, two new granulation strategies were devised to improve the efficiency of computing SCCs. Firstly, four SCC correlations between the vertices were found, which can be divided into two classes. Secondly, two granulation strategies were designed based on correlations between two classes of SCCs. Thirdly, according to the characteristics of the granulation results, the parallelization of computing SCCs was realized. Finally, a parallel algorithm based on granulation strategy for computing SCCs of simple digraphs named GPSCC was proposed. Experimental results show that GPSCC performs with higher computational efficiency than algorithms.

Multi-fuzzy [formula omitted]-covering fusion based accuracy and self-information for feature subset selection

Granular structures are mathematical representations of knowledge used in granular computing. As a new type of granular structure, fuzzy β-covering has attracted widespread attention in recent years. One of the most critical related studies is measuring the uncertainty of fuzzy β-coverings. It is the foundation for studying fuzzy β-covering applications, such as classification and clustering. In this paper, we investigate the uncertainty measures of fuzzy β-coverings from the viewpoints of algebra and information theory, and propose the corresponding methods of fuzzy β-covering reduction for feature selection. Firstly, a generalized fuzzy β-neighborhood and the associated fuzzy β-covering rough sets are presented. Secondly, three types of accuracy measures of fuzzy β-coverings are constructed via fuzzy β-covering rough sets. On this basis, the self-information of fuzzy β-coverings is defined by fusing accuracy and roughness measures. Based on the proposed uncertainty measures, two heuristic methods of fuzzy β-covering reduction are put forward and the corresponding algorithms are designed for monotonic feature selection. Finally, the performance of the proposed methods is compared with several mainstream feature selection methods and experimental results demonstrate the rationality and superiority of our proposed methods.

Multi-association evidential feature selection and its application to identifying schizophrenia

Granular Computing (GrC)-based feature selection can remove redundant features from a massive amount of data and improve the efficiency of information processing. However, the existing method of neighborhood-based information granule only considers the distance between samples, ignoring other significant relationships existing between them. To fill this gap, this paper proposes a novel feature selection approach based on two-step multi-association neighborhood evidence entropy. This approach is constructed in three phases. Firstly, adaptive k value corresponding to each sample in sparse representation method is determined. Sparse correlation and distance measure are fused to form a multi-association information granule. Then, the samples in the multi-association information granule are estimated and weak-related information is removed to constitute a two-step multi-association information granule. Secondly, sparse correlation information is processed using Dempster-Shafer evidence theory, and a new credibility-based function is developed. In addition, the credibility is used to construct a novel neighborhood evidence entropy, which can effectively reflect the uncertainty of data. Thirdly, the proposed neighborhood evidence entropy is applied to assess the importance of features. As a result, several vital features are selected. The experimental results on twelve datasets demonstrate that the effectiveness of the proposed method is superior to other algorithms in construction of information granules and classification accuracy, respectively. Finally, the proposed method is applied to the selection of brain regions in schizophrenia. It can effectively analyze the lesions of schizophrenia and improve the prediction of the disorder. The code is available at https://github.com/fxx-Aurora/TMAE-FS/tree/main.

Efficient cloud data center: An adaptive framework for dynamic Virtual Machine Consolidation

Cloud computing is a thriving and ever-expanding sector in the industry world. This growth has sparked increased interest from organizations seeking to harness its potential. However, the sheer volume of services and offerings in this field has resulted in a noticeable surge in related data. With the rapid evolution and growing demand, cloud computing resource management faces a fresh set of challenges. Resource limitations, such as high maintenance costs, elevated Energy Consumption (EC), and adherence to Service Level Agreements (SLA), are critical concerns for both the cloud computing industry and its user organizations. In this context, taking a proactive approach to resource management and Virtual Machine Consolidation (VMC) has become imperative. The logical management of resources and the consolidation of Virtual Machines (VMs) in a manner that aligns with the requirements and demands of service providers and users have garnered widespread attention. The goal of this proposed paper is to focus on addressing the VMC problem within a unified framework, divided into two main phases. The first phase deals with host workload detection and prediction, while the subsequent phase tackles the selection and allocation of appropriate VMs. In our proposed method, for the first time, we use a Granular Computing (GRC) model, which is an efficient, scalable, and human-centric computational approach. This model exhibits behaviors similar to intelligent human decision-making, as it can simultaneously consider all factors and criteria involved in the problems. We evaluated our proposed method through simulations using CloudSim on various types of workloads. Experimental results demonstrate that our proposed algorithm outperforms other algorithms in all measurement metrics.

Granular computing in zero-divisor graphs of [formula omitted]

In this article, we study the zero-divisor graphs Γ(Zn) of rings of integers modulo n as information systems I(Γ(Zn)) using equivalence classes and rough sets. Equivalence classes are referred as granules and partitions are referred as indiscernible partitions. We define an indiscernibility relation on the vertex set and identify different sets of attributes that induce the same indiscernibility partition. A reduct is a minimal subset of attributes which yields the same partition as the original attribute set. We compute all reducts of the defined information system and classify them in to two types including: (i) the set P of all prime divisors of n and (ii) the set consisting of P∖pi, prime powers of pi in the prime factorization of n and the elements of the form pipj, where pj∈P∖pi. Moreover, we give the structures and the cardinalities of the attribute subsets whose removal yields a different indiscernibility partition than that of the set of all attributes, referred as essential sets. We prove that the essential sets of I(Γ(Zn)) either consist of two prime divisors of n or one prime divisor pi combined with prime powers of pi. Further, we determine the lower and upper approximations of various vertex subsets to study the properties of the zero-divisor graphs. We also study properties of the rough membership function for Γ(Zn). Furthermore, we introduce the class-based discernibility matrix induced by indiscernibility classes of zero divisors and determine general form of its entries. We also prove that the minimal entries of the class-based discernibility matrix coincide with the essential sets of Γ(Zn). Based on these results, we determine information-granularity measures corresponding to the notable partitions of Γ(Zn) and provide an example to establish consistency of the proved results with these well-known measures. Thus, starting from introducing an information system, we investigate the components of granular computing and utilize our findings to compute information granularity measures, contributing to a deeper understanding of the zero divisor graphs via rough set theory.

Augmentation of degranulation mechanism for high-dimensional data with a multi-round optimization strategy

Various fuzzy clustering-based granulation–degranulation techniques have been developed for constructing and optimizing information granules, which help reveal the underlying structure of experimental data in Granular Computing (GrC). Basically, a well-performing granulation–degranulation mechanism runs with a low degranulation (reconstruction) error. However, the increasingly high-dimensional characteristics of data bring great challenges to achieve accurate of reconstruction of high-dimensional data. As such, for the reconstruction of high-dimensional data, an important issue is how to reduce the reconstruction error such that the data could be reconstructed more accurately. In order to address the challenge of unacceptable high reconstruction error posed by the increase in data dimensions and improve the inefficient fuzzy clustering-based granulation in existing techniques, this study develops a multi-round iterative optimization strategy with the use of Fuzzy C-Means (FCM) to enhance reconstruction performance for high-dimensional data. First, we propose a Feature Sampling-based FCM (FS-FCM) scheme served as the granulation mechanism in the framework. The proposed scheme draws on the idea of ensemble learning, where the granulation of original high-dimensional data is accomplished by generating and training low-dimensional sub-datasets through multiple times of feature random sampling. Then, a multi-round iterative granulation–degranulation mechanism is proposed along with its algorithmic framework. Within the proposed framework, we attempt to reduce the reconstruction error by iteratively reconstructing the residual data generated in each round of granulation–degranulation. Finally, we validate the developed strategy framework over twelve publicly available datasets with varying dimension scales. A set of ablation experiments verifies the effectiveness of the FS-FCM granulation scheme. The near-perfect reconstruction performance achieved by the proposed iterative framework on the given datasets further demonstrates its superiority.

An Efficient and Adaptive Granular-Ball Generation Method in Classification Problem.

Granular-ball computing (GBC) is an efficient, robust, and scalable learning method for granular computing. The granular ball (GB) generation method is based on GB computing. This article proposes a method for accelerating GB generation using division to replace k -means. It can significantly improve the efficiency of GB generation while ensuring an accuracy similar to that of the existing methods. In addition, a new adaptive method for GB generation is proposed by considering the elimination of the GB overlap and other factors. This makes the GB generation process parameter-free and completely adaptive in the true sense. In addition, this study first provides mathematical models for the GB covering. The experimental results on some real datasets demonstrate that the two proposed GB generation methods have accuracies similar to those of the existing method in most cases, while adaptiveness or acceleration is realized. All the codes were released in the open-source GBC library at https://www.cquptshuyinxia.com/GBC.html or https://github.com/syxiaa/gbc.

Discovery of Actionable Patterns Through Scalable Vertical Data Split Method with Meta Actions and Information Granules

Action Rules are rule based systems that extract actionable patterns which are hidden in big volumes of data. Users need recommendations on actions they can undertake to increase their profit or accomplish their goals, this recommendations are provided by Actionable patterns. In the technological world of big data, massive amounts of data are collected by organizations, including in major domains like financial, medical, social media and Internet of Things(IoT). To analyze and store such a massive amount of data, distributed computing frameworks like Hadoop and Spark are introduced to store the big data in a distributed fashion which manage and analyze them in parallel. The traditional Action Rules extraction models, which analyze the data in a nondistributed fashion, do not perform well when dealing larger datasets. Serious complications of discovering Action Rules with such distributed environments are - data distribution among computing nodes and calculation of major parameters including : support, confidence, utility, and coverage, that represent the whole data. Information granules form basic entities in the world of Granular Computing(GrC), which represents meaningful smaller units derived from a larger complex information system. In this research, we focus on the data distribution phase of the distributed Actionable Pattern Mining problem. To handle the data distribution task by splitting the big data in both horizontal and vertical fashions - we propose partition threshold rho. In this work, we concentrate on using information granules to implement a vertical data splitting strategy with Meta Actions. Hence our results discover valuable Actionable Knowledge with application in Business and Education domains.

Three-level models of compromised multi-granularity rough sets using three-way decision

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.