Granular Computing Analysis and Design of Intelligent Systems

Information granules, as encountered in natural language, are implicit in nature. To make them fully operational so they can be effectively used to analyze and design intelligent systems, information granules need to be made explicit. An emerging discipline, granular computing focuses on formalizing information granules and unifying them to create a coherent methodological and developmental environment for intelligent system design and analysis. Granular Computing: Analysis and Design of Intelligent Systems presents the unified principles of granular computing along with its comprehensive algorithmic framework and design practices. Introduces the concepts of information granules, information granularity, and granular computing Presents the key formalisms of information granules Builds on the concepts of information granules with discussion of higher-order and higher-type information granules Discusses the operational concept of information granulation and degranulation by highlighting the essence of this tandem and its quantification in terms of the associated reconstruction error Examines the principle of justifiable granularity Stresses the need to look at information granularity as an important design asset that helps construct more realistic models of real-world systems or facilitate collaborative pursuits of system modeling Highlights the concepts, architectures, and design algorithms of granular models Explores application domains where granular computing and granular models play a visible role, including pattern recognition, time series, and decision making Written by an internationally renowned authority in the field, this innovative book introduces readers to granular computing as a new paradigm for the analysis and synthesis of intelligent systems. It is a valuable resource for those engaged in research and practical developments in computer, electrical, industrial, manufacturing, and biomedical engineering. Building from fundamentals, the book is also suitable for readers from nontechnical disciplines where information granules assume a visible position.

Information Granularity, Information Granules, and Granular ComputingInformation Granularity and the Discipline of Granular ComputingFormal Platforms of Information GranularityInformation Granularity and Its QuantificationInformation Granules and a Principle of the Least CommitmentInformation Granules of Higher Type and Higher OrderHybrid Models of Information GranulesA Design of Information GranulesThe Granulation–Degranulation PrincipleInformation Granularity in Data Representation and ProcessingOptimal Allocation of Information GranularityKey Formalisms for Representation of Information Granules and Processing MechanismsSets and Interval AnalysisInterval AnalysisFuzzy Sets: A Departure from the Principle of DichotomyRough SetsShadowed Sets as a Three-Valued Logic Characterization of Fuzzy SetsInformation Granules of Higher Type and Higher Order, and Hybrid Information GranulesFuzzy Sets of Higher OrderRough Fuzzy Sets and Fuzzy Rough SetsType-2 Fuzzy SetsInterval-Valued Fuzzy SetsProbabilistic SetsHybrid Models of Information Granules: Probabilistic and Fuzzy Set Information GranulesRealization of Fuzzy Models with Information Granules of Higher Type and Higher OrderRepresentation of Information GranulesDescription of Information Granules by a Certain Vocabulary of Information GranulesInformation Granulation–Degranulation Mechanism in the Presence of Numeric DataGranulation–Degranulation in the Presence of Triangular Fuzzy SetsThe Design of Information GranulesThe Principle of Justifiable GranularityConstruction of Information Granules through Clustering of Numeric Experimental EvidenceKnowledge-Based Clustering: Bringing Together Data and KnowledgeRefinement of Information Granules through Successive ClusteringCollaborative Clustering and Higher-Level Information GranulesOptimal Allocation of Information Granularity: Building Granular MappingsFrom Mappings and Models to Granular Mappings and Granular ModelsGranular MappingsProtocols of Allocation of Information GranularityDesign Criteria Guiding the Realization of the Protocols for Allocation of Information GranularityGranular Neural Networks as Examples of Granular Nonlinear MappingsFurther Problems of Optimal Allocation of Information GranularityGranular Description of Data and Pattern ClassificationGranular Description of Data—A Shadowed Sets ApproachBuilding Granular Representatives of DataA Construction of Granular Prototypes with the Use of the Granulation–Degranulation MechanismInformation Granularity as a Design Asset and Its Optimal AllocationDesign ConsiderationsPattern Classification with Information GranulesGranular Classification SchemesGranular Models: Architectures and DevelopmentThe Mechanisms of Collaboration and Associated ArchitecturesRealization of Granular Models in a Hierarchical Modeling TopologyThe Detailed Considerations: From Fuzzy Rule-Based Models to Granular Fuzzy ModelsA Single-Level Knowledge Reconciliation: Mechanisms of CollaborationCollaboration Scheme: Information Granules as Sources of Knowledge and a Development of Information Granules of a Higher TypeStructure-Free Granular ModelsThe Essence of Mappings between Input and Output Information Granules and the Underlying ProcessingThe Design of Information Granules in the Output Space and the Realization of the Aggregation ProcessThe Development of the Output Information Granules with the Use of the Principle of Justifiable GranularityInterpretation of Granular MappingsIllustrative ExamplesGranular Time SeriesIntroductory NotesInformation Granules and Time SeriesA Granular Framework of Interpretation of Time Series: A Layered Approach to the Interpretation of Time SeriesA Classification Framework of Granular Time SeriesGranular ClassifiersFrom Models to Granular ModelsKnowledge Transfer in System ModelingFuzzy Logic Networks—Architectural ConsiderationsGranular Logic DescriptorsGranular Neural NetworksThe Design of Granular Fuzzy Takagi–Sugeno Rule-Based Models: An Optimal Allocation of Information GranularityCollaborative and Linguistic Models of Decision MakingAnalytic Hierarchy Process (AHP) Method and Its Granular GeneralizationAnalytic Hierarchy Process Model—The ConceptGranular Reciprocal MatricesA Quantification (Granulation) of Linguistic Terms as Their Operational RealizationGranular Logic OperatorsModes of Processing with Granular Characterization of Fuzzy SetsIndexChapters include Conclusions and References.

Witold Pedrycz, Ph.D., is Professor and Canada Research Chair (CRC) in Computational Intelligence in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. He is also with the Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland and King Abdulaziz University, Saudi Arabia. In 2009, Dr. Pedrycz was elected a foreign member of the Polish Academy of Sciences. He is a Fellow of the Royal Society of Canada, the Institute of Electronic and Electrical Engineers (IEEE), International Fuzzy Systems Association (IFSA), International Society of Management Engineers, Engineers Canada, and The Engineering Institute of Canada. He is editor-in-chief of Information Sciences and editor-in-chief of IEEE Transactions on Systems, Man, and Cybernetics, Part A. He currently serves as an associate editor of IEEE Transactions on Fuzzy Systems and a number of other international journals. In 2007, he received the prestigious Norbert Wiener award from the IEEE Systems, Man, and Cybernetics Society. Dr. Pedrycz is a recipient of the IEEE Canada Computer Engineering Medal. In 2009, he received a Cajastur Prize for Soft Computing from the European Centre for Soft Computing for "pioneering and multifaceted contributions to granular computing." In 2013 he received a prestigious Killam Prize.