Granular computing: perspectives and challenges

A cost-sensitive decision model for efficient pooled testing in mass surveillance of infectious diseases like COVID-19

The COVID-19 pandemic has imposed significant challenges on global health, emphasizing the persistent threat of large-scale infectious diseases in the future. This study addresses the need to enhance pooled testing efficiency for large populations. The common approach in pooled testing involves consolidating multiple test samples into a single tube to efficiently detect positivity at a lower cost. However, what is the optimal number of samples to be grouped together in order to minimize costs? i.e. allocating ten individuals per group may not be the most cost-effective strategy. In response, this paper introduces the hierarchical quotient space, an extension of fuzzy equivalence relations, as a method to optimize group allocations. In this study, we propose a cost-sensitive multi-granularity intelligent decision model to further minimize testing costs. This model considers both testing and collection costs, aiming to achieve the lowest total cost through optimal grouping at a single layer. Building upon this foundation, two multi-granularity models are proposed, exploring hierarchical group optimization. The experimental simulations were conducted using MATLAB R2022a on a desktop with Intel i5-10500 CPU and 8G RAM, considering scenarios with a fixed number of individuals and fixed positive probability. The main findings from our simulations demonstrate that the proposed models significantly enhance the efficiency and reduce the overall costs associated with pooled testing. For example, testing costs were reduced by nearly half when the optimal grouping strategy was applied, compared to the traditional method of grouping ten individuals. Additionally, the multi-granularity approach further optimized the hierarchical groupings, leading to substantial cost savings and improved testing efficiency.

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.

Lateralized Learning to Solve Complex Boolean Problems

Modern classifier systems can effectively classify targets that consist of simple patterns. However, they can fail to detect hierarchical patterns of features that exist in many real-world problems, such as understanding speech or recognizing object ontologies. Biological nervous systems have the ability to abstract knowledge from simple and small-scale problems in order to then apply it to resolve more complex problems in similar and related domains. It is thought that lateral asymmetry of biological brains allows modular learning to occur at different levels of abstraction, which can then be transferred between tasks. This work develops a novel evolutionary machine-learning (EML) system that incorporates lateralization and modular learning at different levels of abstraction. The results of analyzable Boolean tasks show that the lateralized system has the ability to encapsulate underlying knowledge patterns in the form of building blocks of knowledge (BBK). Lateralized abstraction transforms complex problems into simple ones by reusing general patterns (e.g., any parity problem becomes a sequence of the 2-bit parity problem). By enabling abstraction in evolutionary computation, the lateralized system is able to identify complex patterns (e.g., in hierarchical multiplexer (HMux) problems) better than existing systems.

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.

A New Deep-Learning-Based Model for Breast Cancer Diagnosis from Medical Images

Breast cancer is one of the most prevalent cancers among women worldwide, and early detection of the disease can be lifesaving. Detecting breast cancer early allows for treatment to begin faster, increasing the chances of a successful outcome. Machine learning helps in the early detection of breast cancer even in places where there is no access to a specialist doctor. The rapid advancement of machine learning, and particularly deep learning, leads to an increase in the medical imaging community's interest in applying these techniques to improve the accuracy of cancer screening. Most of the data related to diseases is scarce. On the other hand, deep-learning models need much data to learn well. For this reason, the existing deep-learning models on medical images cannot work as well as other images. To overcome this limitation and improve breast cancer classification detection, inspired by two state-of-the-art deep networks, GoogLeNet and residual block, and developing several new features, this paper proposes a new deep model to classify breast cancer. Utilizing adopted granular computing, shortcut connection, two learnable activation functions instead of traditional activation functions, and an attention mechanism is expected to improve the accuracy of diagnosis and consequently decrease the load on doctors. Granular computing can improve diagnosis accuracy by capturing more detailed and fine-grained information about cancer images. The proposed model's superiority is demonstrated by comparing it to several state-of-the-art deep models and existing works using two case studies. The proposed model achieved an accuracy of 93% and 95% on ultrasound images and breast histopathology images, respectively.

Design of Granular Model: A Method Driven by Hyper-Box Iteration Granulation

Recently, granular models have been highlighted in system modeling and applied to many fields since their outcomes are information granules supporting human-centric comprehension and reasoning. In this study, a design method of granular model driven by hyper-box iteration granulation is proposed. The method is composed mainly of partition of input space, formation of input hyper-box information granules with confidence levels, and granulation of output data corresponding to input hyper-box information granules. Among them, the formation of input hyper-box information granules is realized through performing the hyper-box iteration granulation algorithm governed by information granularity on input space, and the granulation of out data corresponding to input hyper-box information granules is completed by the improved principle of justifiable granularity to produce triangular fuzzy information granules. Compared with the existing granular models, the resulting one can yield the more accurate numeric and preferable granular outcomes simultaneously. Experiments completed on the synthetic and publicly available datasets demonstrate the superiority of the granular model designed by the proposed method at granular and numeric levels. Also, the impact of parameters involved in the proposed design method on the performance of ensuing granular model is explored.

A Design of Granular Classifier Based on Granular Data Descriptors

Designing effective and efficient classifiers is a challenging task given the facts that data may exhibit different geometric structures and complex intrarelationships may exist within data. As a fundamental component of granular computing, information granules play a key role in human cognition. Therefore, it is of great interest to develop classifiers based on information granules such that highly interpretable human-centric models with higher accuracy can be constructed. In this study, we elaborate on a novel design methodology of granular classifiers in which information granules play a fundamental role. First, information granules are formed on the basis of labeled patterns following the principle of justifiable granularity. The diversity of samples embraced by each information granule is quantified and controlled in terms of the entropy criterion. This design implies that the information granules constructed in this way form sound homogeneous descriptors characterizing the structure and the diversity of available experimental data. Next, granular classifiers are built in the presence of formed information granules. The classification result for any input instance is determined by summing the contents of the related information granules weighted by membership degrees. The experiments concerning both synthetic data and publicly available datasets demonstrate that the proposed models exhibit better prediction abilities than some commonly encountered classifiers (namely, linear regression, support vector machine, Naïve Bayes, decision tree, and neural networks) and come with enhanced interpretability.

BGRF: A broad granular random forest algorithm

 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.

Application of the Model of Spots for Inverse Problems

This article proposes the application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using deep learning. In general, the spots represent vague figures in abstract "information spaces" or crisp figures with a lack of information about their shapes. However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, based on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Moreover, we defined L4 vectors, L4 matrices, and mathematical operations on them. The developed apparatus can be used in Artificial Intelligence, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates the application of a spot-based inverse Radon algorithm for binary image reconstruction. In both cases, the spot-based algorithms have demonstrated an effective denoising property.

Outlier Detection Based on Fuzzy Rough Granules in Mixed Attribute Data

Outlier detection is one of the most important research directions in data mining. However, most of the current research focuses on outlier detection for categorical or numerical attribute data. There are few studies on the outlier detection of mixed attribute data. In this article, we introduce fuzzy rough sets (FRSs) to deal with the problem of outlier detection in mixed attribute data. Since the outlier detection model of the classical rough set is only applicable to the categorical attribute data, we use FRS to generalize the outlier detection model and construct a generalized outlier detection model based on fuzzy rough granules. First, the granule outlier degree (GOD) is defined to characterize the outlier degree of fuzzy rough granules by employing the fuzzy approximation accuracy. Then, the outlier factor based on fuzzy rough granules is constructed by integrating the GOD and the corresponding weights to characterize the outlier degree of objects. Furthermore, the corresponding fuzzy rough granules-based outlier detection (FRGOD) algorithm is designed. The effectiveness of the FRGOD algorithm is evaluated through experiments on 16 real-world datasets. The experimental results show that the algorithm is more flexible for detecting outliers and is suitable for numerical, categorical, and mixed attribute data.

Optimization of Granulation-Degranulation Mechanism Through Neurocomputing

Information granulation and degranulation play a fundamental role in granular computing (GrC). Given a collection of information granules (referred to as reference information granules), the essence of the granulation process (encoding) is to represent each data (either numeric or granular) in terms of these reference information granules. The degranulation process (decoding) that realizes the reconstruction of original data is associated with a certain level of reconstruction error. An important issue is how to reduce the reconstruction error such that the data could be reconstructed more accurately. In this study, the granulation process is realized by involving fuzzy clustering. A novel neural network is leveraged in the consecutive degranulation process, which could help significantly reduce the reconstruction error. We show that the proposed degranulation architecture exhibits improved capabilities in reconstructing original data in comparison with other methods. A series of experiments with the use of synthetic data and publicly available datasets coming from the machine-learning repository demonstrates the superiority of the proposed method over some existing alternatives.

A Variable-Scale Data Analysis-Based Identification Method for Key Cost Center in Intelligent Manufacturing

Although the competitive advantages brought by intelligent manufacturing technology for enterprises have been preliminarily shown, a lack of matched management capacity still greatly limits its effect. This paper focuses on the cost management capacity problem of intelligent manufacturing enterprises. The multiscale cost data model is established on the basis of the three-dimensional cost system model, which contains actual cost, standard cost, and testing cost. According to the scale transformation theory, we propose the dynamic updating mechanism of standard cost. The key cost center identification methods, respectively, for the production performance assessment scenario (KCCI_PPA) and the business decision-making scenario (KCCI_BDM) are also put forward, which could overcome the subjective determination limitation of initial observation scale in the traditional variable-scale data analysis method. Experiments with both industrial statistical and enterprise real datasets verify the efficiency and accuracy of the proposed KCCI_PPA and KCCI_BDM method.

Decoupling Representation Learning for Imbalanced Electroencephalography Classification in Rapid Serial Visual Presentation Task

OBJECTIVE

The class imbalance problem considerably restricts the performance of electroencephalography (EEG) classification in the rapid serial visual presentation (RSVP) task. Existing solutions typically employ re-balancing strategies (e.g. re-weighting and re-sampling) to alleviate the impact of class imbalance, which enhances the classifier learning of deep networks but unexpectedly damages the representative ability of the learned deep features as original distributions become distorted.

APPROACH

In this study, a novel decoupling representation learning (DRL) model, has been proposed that separates the representation learning and classification processes to capture the discriminative feature of imbalanced RSVP EEG data while classifying it accurately. The representation learning process is responsible for learning universal patterns for the classification of all samples, while the classifier determines a better bounding for the target and non-target classes. Specifically, the representation learning process adopts a dual-branch architecture, which minimizes the contrastive loss to regularize the representation space. In addition, to learn more discriminative information from RSVP EEG data, a novel multi-granular information (MGI) based extractor is designed to extract spatial-temporal information. Considering the class re-balancing strategies can significantly promote classifier learning, the classifier was trained with rebalanced EEG data while freezing the parameters of the representation learning process.

MAIN RESULTS

To evaluate the proposed method, experiments were conducted on two public datasets and one self-conducted dataset. The results demonstrate that the proposed DRL can achieve state-of-the-art performance for EEG classification in the RSVP task.

SIGNIFICANCE

This is the first study to focus on the class imbalance problem and propose a generic solution in the RSVP task. Furthermore, multi-granular data was explored to extract more complementary spatial-temporal information. The code is open-source and available at https://github.com/Tammie-Li/DRL.

A Two-Stage Approach for Constructing Type-2 Information Granules

In this article, we are concerned with the formation of type-2 information granules in a two-stage approach. We present a comprehensive algorithmic framework which gives rise to information granules of a higher type (type-2, to be specific) such that the key structure of the local granular data, their topologies, and their diversities become fully reflected and quantified. In contrast to traditional collaborative clustering where local structures (information granules) are obtained by running algorithms on the local datasets and communicating findings across sites, we propose a way of characterizing granular data (formed) by forming a suite of higher type information granules to reveal an overall structure of a collection of locally available datasets. Information granules built at the lower level on a basis of local sources of data are weighted by the number of data they represent while the information granules formed at the higher level of hierarchy are more abstract and general, thus facilitating a formation of a hierarchical description of data realized at different levels of detail. The construction of information granules is completed by resorting to fuzzy clustering algorithms (more specifically, the well-known Fuzzy C-Means). In the formation of information granules, we follow the fundamental principle of granular computing, viz., the principle of justifiable granularity. Experimental studies concerning selected publicly available machine-learning datasets are reported.

Transformations and information granularity of knowledge structures in set-based granular computing

Granular computing is a relatively new platform for constructing, describing and processing information or knowledge. For crisp information granulation, the universe is decomposed into granules by binary relations on the universe, say, preorder, tolerance and equivalence relations. A knowledge structure is composed of all information granules induced by a relation that corresponds to the granulation. This paper establishes a novel theoretical framework for the measurement of information granularity of knowledge structures. First, two new relations between knowledge structures are introduced through the use of their respective Boolean relation matrices, where the granular equality relation is defined based on an orthogonal transformation with the transformation matrix being a permutation matrix, and the granularly finer relation is presented by combining the classical finer relation and the orthogonal transformation. Then, it is demonstrated that the simplified knowledge structure base with the granularly finer relation is a partially ordered set, which can be represented by a Hasse diagram. Subsequently, an axiomatic definition of information granularity is proposed to satisfy the constraints regarding these two relations. Moreover, a general form of the information granularity is given, and some existing measures are proved to be its special cases. Finally, as an application of the proposed measure, the attribute significance measure is developed based on the information granularity.

A comprehensive model and computational methods to improve Situation Awareness in Intelligence scenarios

This paper presents a comprehensive model for representing and reasoning on situations to support decision makers in Intelligence analysis activities. The main result presented in the paper stems from a work of refinement and abstraction of previous results of the authors related to the use of Situation Awareness and Granular Computing for the development of analysis methods and techniques to support Intelligence. This work made it possible to derive the characteristics of the model from previous case studies and applications with real data, and to link the reasoning techniques to concrete approaches used by intelligence analysts such as, for example, the Structured Analytic Techniques. The model allows to represent an operational situation according to three complementary perspectives: descriptive, relational and behavioral. These three perspectives are instantiated on the basis of the principles and methods of Granular Computing, mainly based on the theories of fuzzy and rough sets, and with the help of further structures such as graphs. As regards the reasoning on the situations thus represented, the paper presents four methods with related case studies and applications validated on real data.