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 discuss 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 electrical engineering, control engineering, electronics and communication engineering, computer sciences, and information sciences.
Volume 1: A Unified Engineering Concept
Notion of Soft Computing
Introduction
Scope for future work
Fuzzy Sets, Fuzzy Operators and Fuzzy Relations
Introduction
Fuzzy set
Metrics for fuzzy numbers
Difference in fuzzy set
Distance in fuzzy set
Cartesian product of fuzzy set
Operators on fuzzy set
Other operations in fuzzy set
Geometric interpretation of fuzzy sets
T-operators
Aggregation operators
Probability versus Possibility
Fuzzy event
Uncertainty
Measure of fuzziness
Type-2 fuzzy sets
Relation
Fuzzy Logic
Introduction
Preliminaries of logic
Lukasiewicz logic
Fuzzy logic
Fuzzy logic as viewed by Zadeh
Algebric structure in fuzzy logic
Critical appreciations on fuzzy logic
Generating logic for fuzzy set
Fuzzifying non-classical logics
Bridging the gap between fuzzy logic and quantum logic
Futuristic ambitions of fuzzy logic
Fuzzy Implications and Fuzzy If-Then Models
Introduction
Syntax and semantics of material implication
Fuzzy modifiers (hedges)
Linguistic truth value
Group decision making based on linguistic decision process
Linguistic assessments and combination of linguistic values
Linguistic preference relations and linguistic choice process
Fuzzy systems as function approximators
Extracting fuzzy rules from sample data points
Fuzzy basis functions
Extracting fuzzy rules from clustering of training samples
Representation of fuzzy IF-THEN rules by petri net
Transformations among various rule based fuzzy models
Losless rule reduction techniques for fuzzy system
Simplification of fuzzy rule base using similarity measure
Qualitative modeling based on fuzzy logic
Rough Set
Introduction
Gateway to roughset concept
Approximation spaces and set approximation
Rough membership function
Information systems
Indiscernibility relation
Some further illustration on set approximation
Dependency of attributes
Approximation and accuracy of classification
Reduction of attributes
Discernibility matrices and functions
Significance of attributes and approximate reducts
Decision rule synthesis
Case study: diagnosis of dengue based on rough set concept
Rough sets, Bayes’ rule & multivalued logic
Rough sets and data mining
Index
Volume 2: Fuzzy Reasoning and Fuzzy Control
Fuzzy Reasoning
Introduction
Model of approximate reasoning
Basic approach to Zadeh’s fuzzy reasoning
Extended fuzzy reasoning
Further extension of fuzzy reasoning
Generalized form of fuzzy reasoning
Application of fuzzy reasoning for prediction of radiation fog
Aggregation in fuzzy system modeling
Single Input Rule Modules (SIRMs) connected fuzzy reasoning method
Some properties of compositional rule of inference
Computation of compositional rule of inference under t-norms
Inverse approximate reasoning
Interpolative fuzzy reasoning
On generalized method-of-case inference rule
Generalized disjunctive syllogism
Ray’s bottom-up inferences
Multidimensional fuzzy reasoning based on multidimensional fuzzy implication
Fuzzy Reasoning Based on Concept of Similarity
Introduction
Fuzzy reasoning using similarity
Similarity based fuzzy reasoning method
Rule reduction is SBR
Proposed similarity measure
Fuzzy reasoning using similarity measures and computational rule of inference
Applications to different models
Reasoning based on total fuzzy similarity
Similarity-based bidirectional approximate reasoning
Logical approaches to fuzzy similarity-based reasoning
Fuzzy resolution based on similarity-based unification
Fuzzy Control
Introduction
Fuzzy controller
Illustration on basic approaches to fuzzy control
Fuzzy associative memory
Fuzzy controller design
Adaptive fuzzy controller design
Self-tuning of fuzzy controller
Single input rule module (SIRM)
Construction of PID controller by simplified fuzzy reasoning method
Fuzzy control as a fuzzy deduction system
Concluding Remarks
Review of the applications and future scope
Index
Biography
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 by Apple Academic Press, Inc.
"This two-volume textbook set is a quite elementary, but rather comprehensive, introduction to the field of soft computing, accessible not only for undergraduates in mathematics, but also for students in computer science and engineering. The presentation is essentially correct, offers figures for most of the notions 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, fuzzy relations, fuzzy logic, fuzzy implications, fuzzy if-then models, and rough sets. Volume 2 covers in separate chapters the topics of fuzzy reasoning, fuzzy reasoning based on the concept of similarity, and fuzzy control."
—Siegfried J. Gottwald, writing in Zentralblatt MATH, 1308