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E-raamat: Granular Computing: Analysis and Design of Intelligent Systems

(University of Alberta, Canada.)
  • Formaat: 309 pages
  • Sari: Industrial Electronics
  • Ilmumisaeg: 03-Sep-2018
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439886878
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  • Formaat: 309 pages
  • Sari: Industrial Electronics
  • Ilmumisaeg: 03-Sep-2018
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439886878
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"Given the nature of the technology, granular computing cuts across a broad range of engineering disciplines. This self-contained book builds upon introductory ideas and provides with illustrative examples that help facilitate a better grasp of more advanced material and enhance its overall presentation. It will be of a particular appeal to those engaged in research and practical developments in computer, electrical, industrial, manufacturing, and biomedical engineering. It will be equally well suited for those coming from non-technical disciplines where information granules assume a highly visible position"--



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.

Arvustused

"Dr. Pedrycz is an internationally acclaimed authority in the granular computing area. ... I particularly appreciate his elegant writing style. This book is the first comprehensive treatise of the granular computing techniques and their application to the design of intelligent systems. ... As an application-oriented practitioner in computational intelligence systems, I think that this book will be a welcome and strongly needed addition to this field. I cannot think of any other expert worldwide more qualified than Prof. Pedycz to write such a book." Emil M. Petriu, University of Ottawa, Canada

"This volume covers most of the interesting and important topics in granular computing. The contents may be well understood by senior or master course students in the field of computer science ... also a good textbook for engineers who are involved in developing so-called intelligent systems." Kaoru Hirota, Tokyo Institute of Technology, Japan

"Dr. Pedryczs latest magnum opus ... breaks new ground in many directions. [ It] takes an important step toward achievement of human-level machine intelligencea principal goal of artificial intelligence (AI) since its inception. ... [ This is] a remarkably well put together and reader-friendly collection of concepts and techniques, which constitute granular computing. ... [ The book] combines extraordinary breadth with extraordinary depth. It contains a wealth of new ideas, and unfolds a vast panorama of concepts, methods, and applications. ... Dr. Pedryczs development and description of these concepts, techniques, and their applications is a truly remarkable achievement. ... must reading for all who are concerned with the design and application of intelligent systems." From the Foreword by Lotfi A. Zadeh, University of California, Berkeley, USA

Preface xiii
The Author xvii
Foreword xix
1 Information Granularity, Information Granules, and Granular Computing
1(18)
1.1 Information Granularity and the Discipline of Granular Computing
1(4)
1.2 Formal Platforms of Information Granularity
5(3)
1.3 Information Granularity and Its Quantification
8(1)
1.4 Information Granules and a Principle of the Least Commitment
9(1)
1.5 Information Granules of Higher Type and Higher Order
10(2)
1.6 Hybrid Models of Information Granules
12(1)
1.7 A Design of Information Granules
12(1)
1.8 The Granulation-Degranulation Principle
13(1)
1.9 Information Granularity in Data Representation and Processing
14(2)
1.10 Optimal Allocation of Information Granularity
16(1)
1.11 Conclusions
16(3)
References
17(2)
2 Key Formalisms for Representation of Information Granules and Processing Mechanisms
19(28)
2.1 Sets and Interval Analysis
19(2)
2.2 Interval Analysis
21(3)
2.3 Fuzzy Sets: A Departure from the Principle of Dichotomy
24(12)
2.3.1 Membership Functions and Classes of Fuzzy Sets
26(2)
2.3.2 Selected Descriptors of Fuzzy Sets
28(3)
2.3.3 Fuzzy Sets as a Family of α - Cuts
31(3)
2.3.4 Triangular Norms and Triangular Conorms as Models of Operations on Fuzzy Sets
34(2)
2.4 Rough Sets
36(3)
2.5 Shadowed Sets as a Three-Valued Logic Characterization of Fuzzy Sets
39(5)
2.5.1 Defining Shadowed Sets
40(2)
2.5.2 The Development of Shadowed Sets
42(2)
2.6 Conclusions
44(3)
References
45(2)
3 Information Granules of Higher Type and Higher Order, and Hybrid Information Granules
47(14)
3.1 Fuzzy Sets of Higher Order
47(3)
3.2 Rough Fuzzy Sets and Fuzzy Rough Sets
50(1)
3.3 Type-2 Fuzzy Sets
51(2)
3.4 Interval-Valued Fuzzy Sets
53(1)
3.5 Probabilistic Sets
54(1)
3.6 Hybrid Models of Information Granules: Probabilistic and Fuzzy Set Information Granules
55(2)
3.7 Realization of Fuzzy Models with Information Granules of Higher Type and Higher Order
57(2)
3.8 Conclusions
59(2)
References
60(1)
4 Representation of Information Granules
61(14)
4.1 Description of Information Granules by a Certain Vocabulary of Information Granules
61(5)
4.2 Information Granulation-Degranulation Mechanism in the Presence of Numeric Data
66(4)
4.3 Granulation-Degranulation in the Presence of Triangular Fuzzy Sets
70(2)
4.4 Conclusions
72(3)
References
72(3)
5 The Design of Information Granules
75(32)
5.1 The Principle of Justifiable Granularity
75(14)
5.1.1 Some Illustrative Examples
79(2)
5.1.2 A Determination of Feasible Values of α
81(3)
5.1.3 Formation of Shadowed Sets or Rough Sets of Information Granules
84(1)
5.1.4 Weighted Data in the Construction of Information Granules
85(1)
5.1.5 From a Family of Interval Information Granules to a Fuzzy Set
86(1)
5.1.6 Development of Fuzzy Sets of Type 2
86(1)
5.1.7 A Design of Multidimensional Information Granules
87(1)
5.1.8 A General View of the Principle of Information Granularity: A Diversity of Formal Setups of Information Granularity
87(2)
5.2 Construction of Information Granules through Clustering of Numeric Experimental Evidence
89(6)
5.3 Knowledge-Based Clustering: Bringing Together Data and Knowledge
95(4)
5.4 Refinement of Information Granules through Successive Clustering
99(2)
5.5 Collaborative Clustering and Higher-Level Information Granules
101(4)
5.6 Conclusions
105(2)
References
105(2)
6 Optimal Allocation of Information Granularity: Building Granular Mappings
107(18)
6.1 From Mappings and Models to Granular Mappings and Granular Models
107(5)
6.2 Granular Mappings
112(2)
6.3 Protocols of Allocation of Information Granularity
114(1)
6.4 Design Criteria Guiding the Realization of the Protocols for Allocation of Information Granularity
115(2)
6.5 Granular Neural Networks as Examples of Granular Nonlinear Mappings
117(4)
6.6 Further Problems of Optimal Allocation of Information Granularity
121(2)
6.6.1 Specificity Maximization through Allocation of Information Granularity
122(1)
6.6.2 Optimal Allocation of Granularity in the Input Space: A Construction of the Granular Input Space
122(1)
6.7 Conclusions
123(2)
References
124(1)
7 Granular Description of Data and Pattern Classification
125(28)
7.1 Granular Description of Data---A Shadowed Sets Approach
125(1)
7.2 Building Granular Representatives of Data
126(11)
7.2.1 A Two-Phase Formation of Granular Representatives
128(3)
7.2.2 Optimization of Information Granularity with the Use of the Particle Swarm Optimization (PSO) Algorithm
131(2)
7.2.3 Some Illustrative Examples
133(4)
7.3 A Construction of Granular Prototypes with the Use of the Granulation-Degranulation Mechanism
137(3)
7.3.1 Granulation and Degranulation Mechanisms in G(x, V1, V2, ..., Vc, U)
139(1)
7.4 Information Granularity as a Design Asset and Its Optimal Allocation
140(2)
7.5 Design Considerations
142(4)
7.5.1 Granular Core and Granular Data Description
142(1)
7.5.2 Selection of a Suitable Value of Information Granularity
142(4)
7.6 Pattern Classification with Information Granules
146(1)
7.7 Granular Classification Schemes
147(4)
7.7.1 Classification Content of Information Granules
149(1)
7.7.2 Determination of Interval-Valued Class Membership Grades
149(1)
7.7.3 Computing Granular Classification Results
150(1)
7.8 Conclusions
151(2)
References
152(1)
8 Granular Models: Architectures and Development
153(32)
8.1 The Mechanisms of Collaboration and Associated Architectures
153(3)
8.2 Realization of Granular Models in a Hierarchical Modeling Topology
156(1)
8.3 The Detailed Considerations: From Fuzzy Rule-Based Models to Granular Fuzzy Models
157(7)
8.4 A Single-Level Knowledge Reconciliation: Mechanisms of Collaboration
164(6)
8.5 Collaboration Scheme: Information Granules as Sources of Knowledge and a Development of Information Granules of a Higher Type
170(3)
8.6 Structure-Free Granular Models
173(1)
8.7 The Essence of Mappings between Input and Output Information Granules and the Underlying Processing
174(1)
8.8 The Design of Information Granules in the Output Space and the Realization of the Aggregation Process
175(2)
8.9 The Development of the Output Information Granules with the Use of the Principle of Justifiable Granularity
177(1)
8.10 Interpretation of Granular Mappings
178(1)
8.11 Illustrative Examples
179(4)
8.12 Conclusions
183(2)
References
184(1)
9 Granular Time Series
185(18)
9.1 Introductory Notes
185(1)
9.2 Information Granules and Time Series
186(1)
9.3 A Granular Framework of Interpretation of Time Series: A Layered Approach to the Interpretation of Time Series
186(6)
9.3.1 Formation of Interval Information Granules
190(1)
9.3.2 Optimization of Temporal Intervals
190(1)
9.3.3 Clustering Information Granules---A Formation of Linguistic Landmarks
191(1)
9.3.4 Matching Information Granules and a Realization of Linguistic Description of Time Series
191(1)
9.4 A Classification Framework of Granular Time, Series
192(6)
9.4.1 Building a Feature Space for Time Series Representation and Classification
196(1)
9.4.2 Formation of a Granular Feature Space
197(1)
9.5 Granular Classifiers
198(3)
9.5.1 Underlying Architecture of the Classifier
198(2)
9.5.2 A Construction of the Fuzzy Relation of the Classifier
200(1)
9.6 Conclusions
201(2)
References
202(1)
10 From Models to Granular Models
203(36)
10.1 Knowledge Transfer in System Modeling
203(3)
10.2 Fuzzy Logic Networks---Architectural Considerations
206(7)
10.2.1 Realization of a Fuzzy Logic Mapping
206(1)
10.2.2 Main Categories of Aggregative Fuzzy Neurons: AND and OR Neurons
207(3)
10.2.3 An Architecture of the Fuzzy Logic Networks
210(2)
10.2.4 Allocation of Information Granularity
212(1)
10.3 Granular Logic Descriptors
213(8)
10.3.1 Logic Descriptors: Quantified and and or Logic Structures
215(2)
10.3.2 The Development of Granular Logic: A Holistic and Unified View of a Collection of Logic Descriptors
217(2)
10.3.3 The Development of the Granular Logic Descriptor in a Feedback Mode
219(2)
10.4 Granular Neural Networks
221(7)
10.4.1 Design Issues of the Granular Neural Networks
224(4)
10.5 The Design of Granular Fuzzy Takagi---Sugeno Rule-Based Models: An Optimal Allocation of Information Granularity
228(8)
10.5.1 General Observations
228(2)
10.5.2 Design of Takagi-Sugeno Fuzzy Models: Some General Views and Common Development Practices
230(1)
10.5.3 Granular Fuzzy Clusters
231(5)
10.5.4 Optimization of Granular Fuzzy Models
236(1)
10.6 Conclusions
236(3)
References
237(2)
11 Collaborative and Linguistic Models of Decision Making
239(32)
11.1 Analytic Hierarchy Process (AHP) Method and Its Granular Generalization
239(2)
11.2 Analytic Hierarchy Process Model---The Concept
241(1)
11.3 Granular Reciprocal Matrices
242(8)
11.3.1 The Objective Function
244(6)
11.4 A Quantification (Granulation) of Linguistic Terms as Their Operational Realization
250(6)
11.4.1 Evaluation of the Mapping from Linguistic Terms to Information Granules
252(4)
11.5 Granular Logic Operators
256(10)
11.5.1 Construction of Information Granules of Membership Function Representation: An Optimization Problem
259(3)
11.5.2 The Optimization Criterion
262(2)
11.5.3 Logic-Consistent Granular Representations of Fuzzy Sets: Experiments
264(2)
11.6 Modes of Processing with Granular Characterization of Fuzzy Sets
266(2)
11.7 Conclusions
268(3)
References
269(2)
Index 271
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.