Soft Computing and Its Applications : Volumes One and Two book cover
1st Edition

Soft Computing and Its Applications
Volumes One and Two

ISBN 9781771880473
Published October 28, 2014 by Apple Academic Press
1100 Pages 169 Color & 198 B/W Illustrations

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Book Description

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.

Table of Contents

Volume 1: A Unified Engineering Concept

Notion of Soft Computing


Scope for future work

Fuzzy Sets, Fuzzy Operators and Fuzzy Relations


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


Aggregation operators

Probability versus Possibility

Fuzzy event


Measure of fuzziness

Type-2 fuzzy sets


Fuzzy Logic


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


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


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


Volume 2: Fuzzy Reasoning and Fuzzy Control

Fuzzy Reasoning


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


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


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


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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