Computer Science

Soft Computing and Its Applications (Set of 2 volumes)
Volume 1: A Unified Engineering Concept
Volume 2: Fuzzy Reasoning and Fuzzy Control

Kumar S. Ray, PhD

Soft Computing and Its Applications (Set of 2 volumes)

Published. Available now.
Pub Date: September 2014
Hardback Price: $389.95 US
Hard ISBN: 9781771880473
Pages: 1100pp w index
Binding Type: hardbound

“Comprehensive introduction of soft computing, accessible not only for undergraduates in mathematics but also for students in computer science and engineering . . . Offers figures for most notations it defines and presents lots of detailed numerical examples. Volume 1 starts with an explanation of the notion of soft computing and continues with chapters on fuzzy sets, fuzzy operators and fuzzy relations, on fuzzy logic, on fuzzy implications and fuzzy if-then models, and on rough sets. Volume 2 covers in separate chapters the topics of fuzzy reasoning, of fuzzy reasoning based on the concept of similarity, and of fuzzy control. The author included also more recent and, occasionally, a bit more advanced topics.”
—Siegfried J. Gottwald (Leipzig), in Zentralblatt MATH 1308

This two-volume set explains the primary tools of soft computing as well as provides an abundance of working examples and detailed design studies. The books start with coverage of fuzzy sets and fuzzy logic and their various approaches to fuzzy reasoning and go on to discusses several advanced features of soft computing and hybrid methodologies. Together they provide a platform for handling different kinds of uncertainties of real life problems. It introduces the reader to the topic of rough sets.

The volumes
  • discuss the present state of art of soft computing
  • include the existing application areas of soft computing
  • present original research contributions
  • discuss the future scope of work in soft computing
This set is unique in that it bridges the gap between theory and practice, and it presents several experimental results on synthetic data and real life data. The books provide a unified platform for applied scientists and engineers in different fields and industries for the application of soft computing tools in many diverse domains of engineering.

The major theme of the volume is to justify the term soft computing, which is essential to handle the vagueness of the real world. The primary tool of soft computing is well discussed with plenty of worked out examples and design studies. The books can be utilized as a standard textbook on soft computing for final-year undergraduate students, postgraduate students, research scholars, professional researchers, and industry R&D groups. The unique feature of the books is that the author clearly presents the state of art with several worked out examples and case studies based on synthetic data and real life data. The application domains of soft computing are also clearly indicated.

The volumes can be used as a textbook and/or reference book by undergraduate and postgraduate students of many different engineering branches, such as, for example, electrical engineering, control engineering, electronics and communication engineering, computer sciences, and information sciences.

Volume 1: A Unified Engineering Concept

Chapter 1. Notion of Soft Computing
- 1.1. Introduction
- 1.2. Scope for future work
Chapter 2. Fuzzy Sets, Fuzzy Operators and Fuzzy Relations
- 2.1. Introduction
- 2.2. Fuzzy set
- 2.3. Metrics for fuzzy numbers
- 2.4. Difference in fuzzy set
- 2.5. Distance in fuzzy set
- 2.6. Cartesian product of fuzzy set
- 2.7. Operators on fuzzy set
- 2.8. Other operations in fuzzy set
- 2.9. Geometric interpretation of fuzzy sets
- 2.10. T-operators
- 2.11. Aggregation operators
- 2.12. Probability versus Possibility
- 2.13. Fuzzy event
- 2.14. Uncertainty
- 2.15. Measure of fuzziness
- 2.16. Type-2 fuzzy sets
- 2.17. Relation
Chapter 3. Fuzzy Logic
- 3.1. Introduction
- 3.2. Preliminaries of logic
- 3.3. Lukasiewicz logic
- 3.4. Fuzzy logic
- 3.5. Fuzzy logic as viewed by Zadeh
- 3.6. Algebric structure in fuzzy logic
- 3.7. Critical appreciations on fuzzy logic
- 3.8. Generating logic for fuzzy set
- 3.9. Fuzzifying non-classical logics
- 3.10. Bridging the gap between fuzzy logic and quantum logic
- 3.11. Futuristic ambitions of fuzzy logic
Chapter 4. Fuzzy Implications and Fuzzy If-Then Models
- 4.1. Introduction
- 4.2. Syntax and semantics of material implication
- 4.3. Fuzzy modifiers (hedges)
- 4.4. Linguistic truth value
- 4.5. Group decision making based on linguistic decision process
- 4.6. Linguistic assessments and combination of linguistic values
- 4.7. Linguistic preference relations and linguistic choice process
- 4.8. Fuzzy systems as function approximators
- 4.9. Extracting fuzzy rules from sample data points
- 4.10. Fuzzy basis functions
- 4.11. Extracting fuzzy rules from clustering of training samples
- 4.12. Representation of fuzzy IF-THEN rules by petri net
- 4.13. Transformations among various rule based fuzzy models
- 4.14. Losless rule reduction techniques for fuzzy system
- 4.15. Simplification of fuzzy rule base using similarity measure
- 4.16. Qualitative modeling based on fuzzy logic
Chapter 5. Rough Set
- 5.1. Introduction
- 5.2. Gateway to roughset concept
- 5.3. Approximation spaces and set approximation
- 5.4. Rough membership function
- 5.5. Information systems
- 5.6. Indiscernibility relation
- 5.7. Some further illustration on set approximation
- 5.8. Dependency of attributes
- 5.9. Approximation and accuracy of classification
- 5.10. Reduction of attributes
- 5.11. Discernibility matrices and functions
- 5.12. Significance of attributes and approximate reducts
- 5.13. Decision rule synthesis
- 5.14. Case study: diagnosis of dengue based on rough set concept
- 5.15. Rough sets, Bayes’ rule & multivalued logic
- 5.16. Rough sets and data mining

Volume 2: Fuzzy Reasoning and Fuzzy Control
Chapter 1. Fuzzy Reasoning
- 1.1. Introduction
- 1.2. Model of approximate reasoning
- 1.3. Basic approach to Zadeh’s fuzzy reasoning
- 1.4. Extended fuzzy reasoning
- 1.5. Further extension of fuzzy reasoning
- 1.6. Generalized form of fuzzy reasoning
- 1.7. Application of fuzzy reasoning for prediction of radiation fog
- 1.8. Aggregation in fuzzy system modeling
- 1.9. Single Input Rule Modules (SIRMs) connected fuzzy reasoning method
- 1.10. Some properties of compositional rule of inference
- 1.11. Computation of compositional rule of inference under t-norms
- 1.12. Inverse approximate reasoning
- 1.13. Interpolative fuzzy reasoning
- 1.14. On generalized method-of-case inference rule
- 1.15. Generalized disjunctive syllogism
- 1.16. Ray’s bottom-up inferences
- 1.17. Multidimensional fuzzy reasoning based on multidimensional fuzzy implication
Chapter 2. Fuzzy Reasoning Based on Concept of Similarity
- 2.1. Introduction
- 2.2. Fuzzy reasoning using similarity
- 2.3. Similarity based fuzzy reasoning method
- 2.4. Rule reduction is SBR
- 2.5. Proposed similarity measure
- 2.6. Fuzzy reasoning using similarity measures and computational rule of inference
- 2.7. Applications to different models
- 2.8. Reasoning based on total fuzzy similarity
- 2.9. Similarity-based bidirectional approximate reasoning
- 2.10. Logical approaches to fuzzy similarity-based reasoning
- 2.11. Fuzzy resolution based on similarity-based unification
Chapter 3. Fuzzy Control
- 3.1. Introduction
- 3.2. Fuzzy controller
- 3.3. Illustration on basic approaches to fuzzy control
- 3.3.1. Fuzzy associative memory
- 3.4. Fuzzy controller design
- 3.5. Adaptive fuzzy controller design
- 3.6 Self-tuning of fuzzy controller
- 3.7. Single input rule module (SIRM)
- 3.8. Construction of PID controller by simplified fuzzy reasoning method
- 3.9. Fuzzy control as a fuzzy deduction system
Chapter 4. Concluding Remarks
- 4.1. Review of the applications and future scope

About the Authors / Editors:
Kumar S. Ray, PhD
Professor, Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India

Kumar S. Ray, PhD, is a professor in the Electronics and Communication Science Unit at the Indian Statistical Institute, Kolkata, India. He is an alumnus of University of Bradford, UK. He was a visiting faculty member under a fellowship program at the University of Texas, Austin, USA. Professor Ray was a member of task force committee of the Government of India, Department of Electronics (DoE/MIT), for the application of AI in power plants. He is the founder and member of Indian Society for Fuzzy Mathematics and Information Processing (ISFUMIP) and a member of Indian Unit for Pattern Recognition and Artificial Intelligence (IUPRAI). In 1991, he was the recipient of the K. S. Krishnan memorial award for the best system-oriented paper in computer vision. He has written a number of research articles published in international journals and has presented at several professional meetings. He also serves as a reviewer of several International journals. His current research interests include artificial intelligence, computer vision, commonsense reasoning, soft computing, non-monotonic deductive database systems, and DNA computing. He is the co-author of two edited volumes on approximate reasoning and fuzzy logic and fuzzy computing, and he is the co-author of Case Studies in Intelligent Computing-Achievements and Trends. He has is also the author of Polygonal Approximation and Scale-Space Analysis of Closed Digital Curves,published Apple Academic Press, Inc.

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