This study elaborates on the role of information granularity in the development of fuzzy controllers. As opposed to numeric data being commonly accepted by fuzzy controllers, we discuss a general processing framework involving data-information granules exhibiting various levels of information granularity. The paper analyzes an impact of information granularity on the performance of the controller. We study a way in which information granules arise in control problems, elaborate on a way of describing these granules as well as provide a way of quantifying the level of information granularity. A number of analysis and design issues are studied including robustness of the fuzzy controller, representation of linguistic information and quantification of its granularity. Nonlinear characteristics of the compiled version of the fuzzy controller operating in presence of granular information are discussed in detail. Illustrative numerical examples are provided as well. ©1999 John Wiley & Sons, Inc.
Foreword.Preface.1. Clustering and Fuzzy Clustering.1. Introduction.2. Basic Notions and Notation.2.1 Types of Data.2.2 Distance and Similarity.3. Main Categories of Clustering Algorithms.3.1 Hierarchical Clustering.3.2 Objective Function - Based Clustering.4. Clustering and Classification.5. Fuzzy Clustering.6. Cluster Validity.7. Extensions of Objective Function-Based Fuzzy Clustering.7.1 Augmented Geometry of Fuzzy Clusters: Fuzzy C-Varieties.7.2 Possibilistic Clustering.7.3 Noise Clustering.8. Self Organizing Maps and Fuzzy Objective Function Based Clustering.9. Conclusions.References.2. Computing with Granular Information: Fuzzy Sets and Fuzzy Relations.1. A Paradigm of Granular Computing: Information Granules and their Processing.2. Fuzzy Sets as Human-Centric Information Granules.3. Operations on Fuzzy Sets.4. Fuzzy Relations.5. Comparison of Two Fuzzy Sets.6. Generalizations of Fuzzy Sets.7. Shadowed Sets.8. Rough Sets.9. Granular Computing and Distributed Processing.10. Conclusions.References.3. Logic-Oriented Neurocomputing.1. Introduction.2. Main Categories of Fuzzy Neurons.2.1 Aggregative Neurons.2.2 Referential (reference) Neurons.3. Architectures of Logic Networks.4. Interpretation Aspects of the Networks.5. The Granular Interfaces of Logic Processing.6. Conclusions.References.4. Conditional Fuzzy Clustering.1. Introduction.2. Problem Statement: Context Fuzzy Sets and Objective Function.3. The Optimization Problem.4. Computational Considerations of Conditional Clustering.5. Generalizations of the Algorithm Through the Aggregation Operator.6. Fuzzy Clustering with Spatial Constraints.7. Conclusions.References.5. Clustering with Partial Supervision.1. Introduction.2. Problem Formulation.3. The Design of the Clusters.4. Experimental Examples.5. Cluster-Based Tracking Problem.6. Conclusions.References.6. Principles of Knowledge-Based Guidance in Fuzzy Clustering.1. Introduction.2. Examples of Knowledge-Oriented Hints and their General Taxonomy.3. The Optimization Environment of Knowledge-Enhanced Clustering.4. Quantification of Knowledge-Based Guidance Hints and Their Optimization.5. The Organization of the Interaction Process.6. Proximity - Based Clustering (P-FCM).7. Web Exploration and P-FCM.8. Linguistic Augmentation of Knowledge-Based Hints.9. Concluding Comments.References.7. Collaborative Clustering.1. Introduction and Rationale.2. Horizontal and Vertical Clustering.3. Horizontal Collaborative Clustering.3.1 Optimization Details.3.2 The Flow of Computing of Collaborative Clustering.3.3 Quantification of the Collaborative Phenomenon of the Clustering.4. Experimental Studies.5. Further Enhancements of Horizontal Clustering.6. The Algorithm of Vertical Clustering.7. A Grid Model of Horizontal and Vertical Clustering.8. Consensus Clustering.9. Conclusions.References.8. Directional Clustering.1. Introduction.2. Problem Formulation.2.1 The Objective Function.2.2 The Logic Transformation Between Information Granules.3. The Algorithm.4. The Overall Development Framework of Directional Clustering.5. Numerical Studies.6. Conclusions.References.9. Fuzzy Relational Clustering.1. Introduction and Problem Statement.2. FCM for Relational Data.3. Decomposition of Fuzzy Relational Patterns.3.1 Gradient-Based Solution to the Decomposition Problem.3.2 Neural Network Model of the Decomposition Problem.4. Comparative Analysis.5. Conclusions.References.10. Fuzzy Clustering of Heterogeneous Patterns.1. Introduction.2. Heterogeneous Data.3. Parametric Models of Granular Data.4. Parametric Mode of Heterogeneous Fuzzy Clustering.5. Nonparametric Heterogeneous Clustering.5.1 A Frame of Reference.5.2 Representation of Granular Data Through the Possibility-Necessity Transformation.5.3 Dereferencing.6. Conclusions.References.11. Hyperbox Models of Granular Data: The Tchebyschev FCM.1. Introduction.2. Problem Formulation.3. The Clustering Algorithm-Detailed Considerations.4. The Development of Granular Prototypes.5. The Geometry of Information Granules.6. Granular Data Description: A General Model.7. Conclusions.References.12. Genetic Tolerance Fuzzy Neural Networks.1. Introduction.2. Operations of Thresholdings and Tolerance: Fuzzy Logic-Based Generalizations.3. The Topology of the Logic Network.4. Genetic Optimization.5. Illustrative Numeric Studies.6. Conclusions.References.13. Granular Prototyping.1. Introduction.2. Problem Formulation.2.1 Expressing Similarity Between Two Fuzzy Sets.2.2 Performance Index (objective function).3. Prototype Optimization.4. The Development of Granular Prototypes.4.1 Optimization of the Similarity Levels.4.2 An Inverse Similarity Problem.5. Conclusions.References.14. Granular Mappings.1. Introduction and Problem Statement.2. Possibility and Necessity measure as the Computational Vehicle of Granular Representation.3. Building the Granular Mapping.4. The Design of Multivariable Granular Mappings Through Fuzzy Clustering.5. Quantification of Granular Mappings.6. Experimental Studies.7. Conclusions.References.15. Linguistic Modeling.1. Introduction.2. The Cluster-Based Representation of the Input - Output Mapping.3. Conditional Clustering in the development of a blueprint of granular models.4. Granular neuron as a Generic Processing Element in Granular Networks.5. The Architecture of Linguistic Models Based on Conditional Fuzzy Clustering.6. Refinements of Linguistic Models.7. Conclusions.References.Bibliography.Index.
In existing granular clustering algorithms, the design of coverage and specificity does not fully capture the inherent structural characteristics of granular data together with the optimization issue, and the current weight setting for the granular data is not sufficient. To address these problems, in this study, the trapezoidal information granule, which is rarely studied before, is concentrated, and we come up with a novel granular clustering algorithm called the weighted possibilistic fuzzy c-means algorithm for trapezoidal granularity (WPFCM-T). Firstly, under the acknowledged principle of justifiable granularity, novel functions of coverage and specificity are designed for trapezoidal information granules, considering the internal characteristics of such granules. The idea of particle swarm optimization (PSO) is exploited to upgrade the established granular data, and then the trapezoidal information granule construction (TIGC) method is proposed to realize granular modeling. Secondly, an exponential weight is constructed with regard to coverage and specificity, while a novel distance via α-cuts is given. The possibilistic fuzzy c-means (PFCM) structure is introduced into granular clustering, in which the new weight and distance are integrated, resulting in the proposed WPFCM-T algorithm. Thirdly, the reconstruction criterion is studied to evaluate granular clustering, and hence an overall framework including granular modeling, clustering and evaluation is constructed. Lastly, through experiments completed on artificial datasets, UCI datasets, large datasets, high-dimensional datasets, and noisy datasets, WPFCMT has superior granular data reconstruction ability by contrast with other granular clustering algorithms, indicating that the granular clustering performance of WPFCM-T is better than the others.
In recent years, we have been witnessing the truly remarkable phenomenon of social networks, which have emerged as a new way of modern Web-based communication. By generating enormously large volumes of data, social networks have triggered a great deal of interest both among the research community of data mining and knowledge discovery and professionals directly involved in delivering technologies and services of social networks. Social networks, along with their diversified media, have brought to existence a vast array of unique and far-reaching opportunities, as well as inevitable challenges. Those have been manifesting at both the conceptual and technological level. To fully unleash the potential of social networks while minimizing any adverse effects and alleviate possible pitfalls, innovative and efficient solutions become extremely timely. WIREs Data Mining and Knowledge Discovery has been at the forefront of disseminating current, comprehensive reviews of the pioneering research that is being done on data mining. Now, a new initiative has been launched. It comes in the form of collections of prudently organized and authoritative studies on data mining and social networks. The ultimate objective behind this new initiative is to offer the reader a curated set of articles spanning across a broad spectrum of topics that are arranged in a useful and meaningful way to address the vital issues of social networks from the perspective of data mining. The collection demonstrates a comprehensive analysis of networks and looks at the complex patterns of dynamics resulting in communities and calling for their mining, identifying leader formations, discovering patterns of interactions, and studying sentiment mining. Other articles discuss the associated problems of identity management, coping with fake identities, detection of fake news, credibility assessment, and deceptive engagement. I hope that all of our readers will find this collection interesting and educational.
In this study, we propose a new concept of granular rule-based models whose rules assume a format ``if G(A i ) then G(f i )'' where G$(.)s are granular generalizations of the numeric conditions and conclusions of the rules. Those generalizations can be expressed e.g., in terms of interval-valued, type-2 or probabilistic fuzzy sets. We discuss several classes of fuzzy models depending upon available information granules and offer a motivation present behind their emergence. The design of these granular architectures exploits the essentials of Granular Computing such as a principle of justifiable granularity and an optimal allocation of information granularity. Detailed investigations of the performance indexes (objective functions) along with the related optimization schemes are covered as well.
