An Introduction to Fuzzy Set Theory and Fuzzy Logic, 2/e

Contents:

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 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 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 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 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 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 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 15. Intuitionistic Fuzzy Sets, Rough Sets, Vague Sets and Soft Sets • Introduction • Intuitionistic Fuzzy Sets • Special Classes of Intuitionistic Fuzzy Sets • (a, ??) 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

About the Author:

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.