1st Edition

Soft Computing and Its Applications Volumes One and Two

    1100 Pages 169 Color & 198 B/W Illustrations
    by Apple Academic Press

    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


    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



    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