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Granular Computing An Introduction

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ISBN-10: 1402072732

ISBN-13: 9781402072734

Edition: 2003

Authors: Andrzej Bargiela, Witold Pedrycz

List price: $279.99
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Description:

Granular computing is a conceptual paradigm of information processing, motivated by the need for intelligent processing of empirical data into a manageable abstract knowledge. This title starts with the basic methodology, through algorithms and granular worlds, to a representative spectrum of applications.
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Book details

List price: $279.99
Copyright year: 2003
Publisher: Springer
Publication date: 11/30/2002
Binding: Hardcover
Pages: 452
Size: 6.55" wide x 9.25" long x 1.00" tall
Weight: 1.694
Language: English

Preface
Methodology and Mathematical Framework
Granular Computing as an Emerging Prardigm of Information Processing
Introductory comments
Information granules are everywhere
Spatial granulation: Image processing and GIS
Temporal granulation
Formal models of information granules
Conceptual aspects of information granules
Size of information granules and their relevance
Usefulness of information granules
Defining a granular world
Granular computing: An information processing pyramid
Communication between granular worlds
Fundamental issues of traversing information pyramid: Encoding and decoding
Interoperability between different formal platforms of information granules
Conclusions
References
Sets and intervals
Historical background
The formalism of sets
Basic set operations
Functional mapping of sets
Arithmetical operations on sets
Set enclosure
Interval analysis
Basic interval operations
Arithmetical operations on intervals
Interval vectors
Interval matrices
Enclosure of functions
Centered enclosures
Space subdivision enclosures
Conclusions
References
Fuzzy Sets
The concept and formalism
The description and geometry of fuzzy sets
Main classes of membership functions
Operations on fuzzy sets
Information granularity and fuzzy sets
Relationships between fuzzy sets in the same space
Fuzzy sets and linguistic variables
Transformations of fuzzy sets in the same space
Fuzzy arithmetic
Fuzzy relations and relational calculus
Fuzzy sets and multivalued logic
Calibration of fuzzy sets
The embedding principle
Conclusions
References
Rough Sets
Introduction
The concept
Information systems
Rough sets as set approximations
Characterization of rough sets
Set comparisons in the setting of rough sets
Reduction of attribute spaces and reducts
Rough functions
Conclusions
References
Generalisations of Information Granules
Interval-valued fuzzy sets
Fuzzy sets of type-2 and higher orders
Fuzzy sets of level-2 and higher
Fuzzy sets and rough sets
Shadowed sets
Operations on shadowed sets
Transformations of shadowed sets
Probabilistic sets
Intuitionistic fuzzy sets
Probability of granular constructs: Granularity and their experimental relevance
Concluding comments
References
Algorithms of Information Granulation
From Numbers to Information Granules
Introductory comments
Information granules and information granulation
The principle of granular clustering
Conceptual design
Interpretation and validation of granular clustering
The computational aspects of granular computing
Defining compatibility between information granules
Expressing inclusion of information granules
The granular analysis
Characterization of hyperboxes
Granular feature analysis
Experimental studies
Synthetic data
Boston housing data
Conclusions
References
Recursive Information Granulation
Introduction
Example application domains
Information granules: Design and characterization
Building set-based information granules
Assessment and interpretation of information granule through fuzzy clustering
Granular time series
Time-domain granulation
Phase-space granulation
Numerical studies
Conclusions
References
Granular Prototyping in Fuzzy Clustering
Introduction
Problem formulation
Expressing similarity between two fuzzy sets
Performance index (objective function)
Prototype optimisation
The development of granular prototypes
Optimization of the similarity levels
An inverse similarity problem
Conclusions
References
Logic-Based Fuzzy Clustering
Introduction and problem formulation
The algorithm
Experimental studies
Conclusions
References
Semantical Stability of Information Granules
Introduction
Information granulation: Design and validation
Set approximation of fuzzy sets
Algorithmic issues of information granulation: Design and validation
The design of fuzzy sets - information granules
The validation phase
Experiments
Synthetic one-dimensional data
Real-world data
Conclusions
References
Granular World Communications
Communications between granular worlds: Fundamentals
Introduction
Representation of fuzzy sets in the set-theoretic framework
Communication with a numeric world
Conclusions
References
Networking of Granular Worlds: Collaborative Clustering
Introduction
The horizontal collaborative clustering
The notation
Optimization details of the collaborative clustering
The detailed clustering algorithm: A flow of computing
Quantification of the collaborative phenomenon of the clustering
Numerical examples of horizontal collaboration
Vertical collaborative clustering
The clustering algorithm
Numerical experiments with vertical collaboration
Vertical and horizontal clustering: Collaboration space and data confidentiality and security
Conclusions
References
Directional Models of Granular Communication
Introduction
Problem formulation
The objective function and its generalization
The logic transformation
The algorithm
The overall development framework: A flow of optimisation activities
Experimental studies
Conclusions
References
Intelligent Agents and Granular Worlds
Introduction
Communication between the agents in the granular environment
A fuzzy state machine as a generic model of an intelligent agent
The fuzzy JK flip-flop and its dynamics
The development of Moore type fuzzy state machines
The architecture
A logic processor and its detailed topology
A fuzzy Moore state machine
The learning scheme
Conclusions
References
Granular Systems Applications
Self-Organising Maps in the Design and Processing of Granular Information
Introduction
Self-organizing maps
Revealing structure in data by cluster growing
Associated self-organizing maps
Weight maps
Region (clustering) map
Data distribution map
Experiments--Synthetic and Machine Learning data
Case study: Analysis of software quality via software measures
Software measures
Visualising relationships between software measures with SOMs
Case study: A granular analysis of ECG data
Conclusions
References
Temporal Granulation and Signal Analysis
Introductory notes
Granulation of signals in spatial domain
The development of data-justifiable information granules: A formulation
The detailed granulation algorithm
Granular models of signals
Predictive description of granular models
Condensation of numeric signals
Experimental studies
Rough sets in signal granulation
Conclusions
References
Granular Data Compression
Introduction
Fuzzy relational equations: A brief overview
Relational calculus in image compression
Experiments
Conclusions
References
Interval State Estimation in Systems Modelling
Introduction
Estimation of the state uncertainty set
Monte Carlo method
Linear Programming method
Ellipsoid method
Sensitivity Matrix method
Real-life application
Conclusions
References
Epilogue
Index