Handbook of Granular Computing

Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years have witnessed a renewed and expanding interest in the topic as it begins to play a key role in bioinformatics, e-commerce, machine learning, security, data mining and wireless mobile computing when it comes to the issues of effectiveness, robustness and uncertainty. The Handbook of Granular Computing offers a comprehensive reference source for the granular computing community, edited by and with contributions from leading experts in the field.

• Includes chapters covering the foundations of granular computing, interval analysis and fuzzy set theory; hybrid methods and models of granular computing; and applications and case studies.
• Divided into 5 sections: Preliminaries, Fundamentals, Methodology and Algorithms, Development of Hybrid Models and Applications and Case Studies.
• Presents the flow of ideas in a systematic, well-organized manner, starting with the concepts and motivation and proceeding to detailed design that materializes in specific algorithms, applications and case studies.
• Provides the reader with a self-contained reference that includes all pre-requisite knowledge, augmented with step-by-step explanations of more advanced concepts.

The Handbook of Granular Computing represents a significant and valuable contribution to the literature and will appeal to a broad audience including researchers, students and practitioners in the fields of Computational Intelligence, pattern recognition, fuzzy sets and neural networks, system modelling, operations research and bioinformatics.

Table of Contents

Part One Fundamentals and Methodology of Granular Computing Based on Interval Analysis, Fuzzy Sets and Rough Sets
Chapter 1 Interval Computation as an Important Part of Granular Computing: An Introduction
Chapter 2 Stochastic Arithmetic as a Model of Granular Computing
Chapter 3 Fundamentals of Interval Analysis and Linkages to Fuzzy Set Theory
Chapter 4 Interval Methods for Non-Linear Equation Solving Applications
Chapter 5 Fuzzy Sets as a User-Centric Processing Framework of Granular Computing
Chapter 6 Measurement and Elicitation of Membership Functions
Chapter 7 Fuzzy Clustering as a Data-Driven Development Environment for Information Granules
Chapter 8 Encoding and Decoding of Fuzzy Granules
Chapter 9 Systems of Information Granules
Chapter 10 Logical Connectives for Granular Computing
Chapter 11 Calculi of Information Granules. Fuzzy Relational Equations
Chapter 12 Fuzzy Numbers and Fuzzy Arithmetic
Chapter 13 Rough-Granular Computing
Chapter 14 Wisdom Granular Computing
Chapter 15 Granular Computing for Reasoning about Ordered Data: The Dominance-Based Rough Set Approach
Chapter 16 A Unified Approach to Granulation of Knowledge and Granular Computing Based on Rough Mereology: A Survey
Chapter 17 A Unified Framework of Granular Computing
Chapter 18 Quotient Spaces and Granular Computing
Chapter 19 Rough Sets and Granular Computing: Toward Rough-Granular Computing
Chapter 20 Construction of Rough Information Granules
Chapter 21 Spatiotemporal Reasoning in Rough Sets and Granular Computing
Part Two Hybrid Methods and Models of Granular Computing
Chapter 22 A Survey of Interval-Valued Fuzzy Sets
Chapter 23 Measurement Theory and Uncertainty in Measurements: Application of Interval Analysis and Fuzzy Sets Methods
Chapter 24 Fuzzy Rough Sets: From Theory into Practice
Chapter 25 On Type 2 Fuzzy Sets as Granular Models for Words
Chapter 26 Design of Intelligent Systems with Interval Type-2 Fuzzy Logic
Chapter 27 Theoretical Aspects of Shadowed Sets
Chapter 28 Fuzzy Representations of Spatial Relations for Spatial Reasoning
Chapter 29 Rough–Neural Methodologies in Granular Computing
Chapter 30 Approximation and Perception in Ethology-Based Reinforcement Learning
Chapter 31 Fuzzy Linear Programming
Chapter 32 A Fuzzy Regression Approach to Acquisition of Linguistic Rules
Chapter 33 Fuzzy Associative Memories and Their Relationship to Mathematical Morphology
Chapter 34 Fuzzy Cognitive Maps
Part Three Applications and Case Studies
Chapter 35 Rough Sets and Granular Computing in Behavioral Pattern Identification and Planning
Chapter 36 Rough Sets and Granular Computing in Hierarchical Learning
Chapter 37 Outlier and Exception Analysis in Rough Sets and Granular Computing
Chapter 38 Information Access and Retrieval
Chapter 39 Granular Computing in Medical Informatics
Chapter 40 Eigen Fuzzy Sets and Image Information Retrieval
Chapter 41 Rough Sets and Granular Computing in Dealing with Missing Attribute Values
Chapter 42 Granular Computing in Machine Learning and Data Mining
Chapter 43 On Group Decision Making, Consensus Reaching, Voting, and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and a Granulation Perspective
Chapter 44 FuzzJADE: A Framework for Agent-Based FLCs
Chapter 45 Granular Models for Time-Series Forecasting
Chapter 46 Rough Clustering