Title An Introduction to Fuzzy Set Theory and Fuzzy Logic, 2/e
Subtitle
Author Chander Mohan
ISBN 9789387153691
List price Rs 1295.00
Price outside India Available on Request
Original price
Binding Hardbound
No of pages 392
Book size 152 x 228 mm
Publishing year 2018
Original publisher Viva Books Private Limited
Published in India by Viva Books Private Limited
Exclusive distributors Viva Books Private Limited
Sales territory Worldwide
Status New Arrival
About the book
  
 

Description:

This book presents the rudiments of fuzzy set theory and fuzzy logic and related topics and their applications in a simple and easy-to-understand manner. Written with a general type of reader in mind, the book avoids the extremes of abstract mathematical proofs as well as specialized technical details of different areas of application. The book is intended to motivate the readers in getting a clear grasp of the basic concepts of the subject and its possible applications. A special feature of the book is that the exercises at the end of each chapter are preceded by a set of short-answer review-type questions. These are intended to help the reader in developing the confidence that he/she has correctly grasped the concepts introduced in the chapter. The book can be used as a text for the study of the topics of fuzzy set theory, fuzzy logic and their possible applications at the undergraduate, graduate and postgraduate students of mathematics, engineering and other disciplines of science, arts and medicine.

In this book:

                • Introduction

                • Fuzzy Sets

                • Operations on Fuzzy Sets

                • Fuzzy Numbers

                • Fuzzy Relations and Fuzzy Graphs

                • Fuzzy Functions and Calculus of Fuzzy Functions

                • Measures of Vagueness and Uncertainty

                • Evidence Theory, Possibility Theory and Probability Theory

                • Linguistic Variables, Fuzzy Rules and Fuzzy Propositions

                • Fuzzy Logic and Approximate Reasoning

                • Decision Making in a Fuzzy Environment

                • Construction of Fuzzy Sets and Defuzzification

                • Fuzzy Rules Based Models and Fuzzy Systems

                • Engineering and Other Applications

                • Intutionistic Fuzzy Sets, Rough Sets, Vague Sets and Soft Sets

 

Contents:

Preface to the Second Edition

Preface to the First Edition

Acknowledgements

Chapter 1. Introduction • Limitations of the Conventional Tools of Analysis • Certainty Versus Uncertainty • Nature and Role of Uncertainty • Fuzzy Set Theory and Related Concepts • About This Book

Chapter 2. Fuzzy Sets • Classical Sets: An Overview • Extensional Definition • Intensional Definition • Characteristic Functional Definition • Fuzzy Sets: Why do we need them • Fuzzy Sets • Other Representations of Fuzzy Sets • There is nothing fuzzy about Fuzzy Sets • Properties of Fuzzy Sets • Cardinality and relative cardinality • Height • Support of a fuzzy set • a-cuts • Compliment of a Fuzzy Set • Equal Fuzzy Sets • Universal Set, Empty Set and Crossover Point • Failing of the Law of Excluded Middle and the Law of Contradiction • Subset of a Fuzzy Set • Convex Fuzzy Sets • Geometric Interpretation of Fuzzy Sets • Features of Membership Function • Some Well Known Membership Functions • Triangular Membership Function • Trapezoidal Membership Function • Bell-shaped, Gaussian and Sigmoidal membership Functions • Some other commonly used Membership Functions • Short Answer Review Questions • Exercises

Chapter 3. Operations on Fuzzy Sets • Introduction • Operations on Crisp Sets • Operations on FuzzySets • Union and Intersection of Fuzzy Sets • Algebraic Sum, Bounded Sum and Bounded Difference • Algebraic Product • Power of a Fuzzy Set • Some other Operations on Fuzzy Sets • Convex Combination of Fuzzy Sets • Operations on Fuzzy Sets Defined on Different Universes of Discourse • Cartesian Product • Extension Principle • t-Norm and t-Conorm Operations • Certain t-norm and t-conorm Operations • Pairs of t-norm and t-conorm Operations • Some well-known pairs of t-norm and t-conorm Operations • Generation of t-norm and t-Conorm operations • Short Answer Review Questions • Exercises

Chapter 4. Fuzzy Numbers • Introduction • Fuzzy Numbers • Positive and Negative Fuzzy Numbers • Fuzzy Numbers of LR Type • Triangular and Trapezoidal Fuzzy Numbers • Arithmetic Operations on Fuzzy Numbers • Operations on Fuzzy Numbers on the Basis of Extension Principle • Addition, Subtraction, Multiplication and Division Operations • Operations on Fuzzy Numbers of LR type • Arithmetic Operations on Fuzzy Numbers Based on a-Cuts • Ordering of Fuzzy Numbers • Fuzzy Equations • Solution of Fuzzy Equations of Type à ? X? = B? and à ? X? = B? • Solution of Fuzzy Equations of the Type à ? X? = B?, à X? = B? • Conditions for Existence of Solutions • Short Answer Review Questions • Exercises

Chapter 5. Fuzzy Relations and Fuzzy Graphs • Introduction • Fuzzy Relations on Crisp Sets • Fuzzy Relations as Matrices • Fuzzy Relations on Fuzzy Sets • Domain and Range of a Fuzzy Relation • Union and Intersection of Fuzzy Relations • Projections and Cylindrical Extensions • Projection • Cylindrical Extension • Composition of Fuzzy Relations • The max-min, max-product and max-average compositions • Properties of max-min Composition • Relational Join • Symmetric and Anti Symmetric Relations • Transitivity • Transitive Closure of a Fuzzy Relation R~(X, X) • Fuzzy Graph • Special Fuzzy Relations • Similarity Relations • Fuzzy Ordering Relations • Fuzzy Compatibility Relations • Fuzzy Morphisms • Fuzzy Relation Equations • Short Answer Review Questions • Exercises

Chapter 6. Fuzzy Functions and Calculus of Fuzzy Functions • Introduction • Fuzzy Functions • Correspondence between a Fuzzy Function and a Fuzzy Relation • Inverse of a Fuzzy Function • Extrema of Fuzzy Functions • Integration of Fuzzy Functions • Integration of a Fuzzy Function Over a Crisp Interval • Properties of Integrals of Fuzzy Functions • Integration of a Crisp Real Valued Function Over a Fuzzy Interval • Properties of Integrals of Crisp Functions Over Fuzzy Intervals • Differentiation of a Fuzzy Function • Properties of Derivatives of Crisp Functions at Fuzzy Points • Short Answer Review Questions • Exercises

Chapter 7. Measures of Vagueness and Uncertainty • Introduction • Fuzzy Measures • Difference between a Fuzzy Measure and a Measure of Fuzziness • Uncertainty Based Information • Non - Specificity of Crisp Sets • Non-specificity of Fuzzy Sets • Fuzziness of Fuzzy Sets • Fuzziness as Lack of Distinction Between a Set and Its Complement • Non-specificity Versus Fuzziness • Short Answer Review Questions • Exercises

Chapter 8. Evidence Theory, Possibility Theory and Probability Theory • Introduction • Evidence Theory • Possibility Theory • Possibility Distributions • Possibility Measure • U-Uncertainty of Possibility Distributions • Joint Possibility Distributions • Relationship Between Possibility Distributions and Probability Distributions • Relationship Between Possibility and Necessity • Fuzzy Sets and Possibility Theory • Possibility Theory Versus Probability Theory • Non-interactiveness Versus Independence • Measures of Non-specificity in Probability Theory • Probability of a Fuzzy Event • Conditional Probability of Fuzzy Events • Independent Fuzzy Events • Bayes’ Theorem for Fuzzy Events • Fuzzy Probability • Probabilistic Interpretation of Fuzzy Sets • Possibility Measures and Probability Measures as Fuzzy Measures • Principle of Uncertainty Invariance • Short Answer Review Questions • Exercises

Chapter 9. Linguistic Variables, Fuzzy Rules and Fuzzy Propositions • Introduction • Linguistic Variables • Linguistic Variables ‘Truth’ and ‘Probable’ • Hedges • Structured Linguistic Variables • Boolean Linguistic Variables • Quantifiers • Fuzzy Rules • Fuzzy Mapping Rule • Fuzzy Implication Rules • Fuzzy Propositions • Unconditional and Unqualified Propositions • Unconditional and Qualified Propositions • Conditional and Unqualified Propositions • Conditional and Qualified Propositions • Short Answer Review Questions • Exercises

Chapter 10. Fuzzy Logic and Approximate Reasoning • Introduction • Classical Logic: An Overview • Truth Tables of Classical Logic • Modus Ponens and Modus Tolens • Propositional Logic • First Order Predicate Calculus • Multivalued Logic • Fuzzy Logic • Fuzzy Truth Tables • Baldwin’s Version of Fuzzy Logic • Inference from Conditional Fuzzy Propositions • Inference from Conditional and Quantified Propositions • Inference from Fuzzy Quantified Propositions • Fuzzy Implications • Fuzzy Implication Rules • Criteria of Fuzzy Implications • Families of Fuzzy Implications • Approximate Reasoning • Short Answer Review Questions • Exercises

Chapter 11. Decision Making in a Fuzzy Environment • Introduction • Individual Decision Making • Trade-off Between Goals and Constraints • Multiperson Decision Making • Multicriteria Decision Making • Multiperson-Multicriteria Decision Making • Fuzzy Ranking of Alternatives • Optimization in a Fuzzy Environment • Fuzzy Linear Programming • Multistage Decision Making • Short Answer Review Questions • Exercises

Chapter 12. Construction of Fuzzy Sets and Defuzzification • Introduction • Necessity for Fuzzification • Construction of Fuzzy Sets • Methods for Constructing Membership Functions • Direct Methods with Single Expert • Direct Methods with Multiple Experts • Indirect Methods with Single Expert • Indirect Methods with Multiple Experts • Construction from Sample Data • Fusion of Local Models • Defuzzification • Mean of Maximum (MOM) Method • Centre-of-Area (COA) Method • The Height Method • Centre of Maxima Method • Parameterized Family of Defuzzification Methods • Short Answer Review Questions • Exercises

Chapter 13. Fuzzy Rules Based Models and Fuzzy Systems • Introduction • Fuzzy Rules Based Inference • Fuzzy Rules Based Models • Fuzzy Partition • Mapping a Fuzzy Subspace to Local Models • Different Types of Fuzzy Rule-based Models • The Mamdani Model • The TSK Model • Standard Additive Model • Fuzzy Systems • Fuzzy Expert Systems • Fuzzy Controllers • A Fuzzy Controller • Fuzzy Automata • Short Answer Review Questions • Exercises

Chapter 14. Engineering and Other Applications • Introduction • Engineering Applications • Civil Engineering • Mechanical Engineering • Industrial Engineering • Electrical Engineering • Computer Engineering • Reliability Theory • Pattern Recognition, Cluster Analysis and Image Processing • Robotics • Other Engineering Applications • Applications in Other Disciplines • Medicine • Economics • Fuzzy Regression • Genetic Algorithms • Neural Networks • Soft Computing • Interpersonal Communication • Natural Sciences • Psychology • Languages • Miscellaneous • Exercises

Chapter 15. Intuitionistic Fuzzy Sets, Rough Sets, Vague Sets and Soft Sets • Introduction • Intuitionistic Fuzzy Sets • Special Classes of Intuitionistic Fuzzy Sets • (a, ß) cut of an IFS • Construction of an Intuitionistic Fuzzy Set from a Fuzzy Set • Intuitionistic Fuzzy Numbers (IFN) • Arithmetic Operations onIFN’s • Vague Sets • Difference between IFS and VS • Algebraic Operations on Vague Sets • Soft Sets • Operation on Soft Sets • Fuzzy Soft Sets • Vague Soft Sets • Rough Sets • Vagueness and Uncertainty in Rough Sets • Uncertainty of Rough Sets • Fuzzy Rough Sets and Rough Fuzzy Sets • Short Answer Review Questions • Exercises

Bibliography

Index

 

About theAuthor:

Prof. Chander Mohan was born on 8 October 1939 in Jhelum, British India, now on Pakistan. He completed his B.A. (Honours) in Mathematics in 1957 and M.A. in Mathematics in 1960 from Panjab University, Chandigarh, India. He obtained his Ph.D. in Mathematics from the University of Roorkee, India in 1967. He taught at Multanimal Modi College, Modinagar, India, as Lecturer in Mathematics during 1961–64. Thereafter he taught at the Department of Mathematics, University of Roorkee, as Lecturer (1964–70); as Reader (1970–85); and as Professor (1985–2000). He was also Head of the Department during 1994–99. He has also served as Professor and Dean, Amity School of Computer Science, Noida, Uttar Pradesh, India (2000–02); as Professor and Head, Mathematics Department, I.I.L.M. College of Engineering and Technology, Greater Noida, Uttar Pradesh, India (2002–04). Currently, he is Professor Emeritus, Department of Computer Science, Ambala College of Engineering and Applied Research, Ambala, Haryana, where he has been teaching since 2004. He has over 90 research publications in national and international research journals and three books on technical subjects to his credit. He is also the recipient of the Khosla Research Award in 1990 and Millennium Award of Honour of the American Biographical Institute. He is listed in the Who’s Who publications. He is a member of the International Astronomical Union, Operations Research Society of India (Founder Member), Indian Astronomical Society (Founder Member), Indian Society for Industrial and Applied Mathematics (Executive Committee Member), and honorary chair, Indian Society of Soft Computing.

 

Target Audience:

The book can be used as a text for the study of the topics of fuzzy set theory, fuzzy logic and related concepts and their applications both at the undergraduate and postgraduate level in mathematics and other disciplines of science, arts, engineering and medicine.

 

 
Special prices are applicable to the authorised sales territory only.
Prices are subject to change without prior notice.