From Classical (Crisp) Sets to Fuzzy sets: A Grand Paradigm Shift: Crisp sets an overview, Fuzzy sets: Basic type, Basic concepts, Fuzzy sets Versus Crisp sets: Additional properties of α cuts, Representation of fuzzy sets, Extension principle for fuzzy sets
Operations on Fuzzy sets: Types of operations, Fuzzy complements, Fuzzy inster sections: t – norms, Fuzzy union: t – conforms, combination of operations.
Fuzzy numbers, Linguistic variables, Arithmetic operation on intervals, Arithmetic operation on fuzzy numbers, Fuzzy equations
Fuzzy relations: Binary fuzzy relations, Binary relations on a single set, Fuzzy equivalence relations, fuzzy compatibility relations, Fuzzy ordering relations, Fuzzy morphisms.
Fuzzy relation equations: General discussion, Problem portioning, Solution method, Fuzzy relation equations based on Sup I Compositions, Fuzzy relation equations based on Inf –wi Compositions.
Reference Book:
1. Fuzzy Sets by George J. Klir and Tina A. Folger, Uncertainty and Information, Prentice-Hall of India Private Limited-Fourth printing-June 1995 2. Fuzzy Logic with Engineering Applications by Ross, 2nd Edition, Wiley Publications, 2009. 3. Networks, Fuzzy Logic & Genetic Algorithms by S. Rajasekaran, G.A. Vijayalakshmi Pai, Neural PHI Publications, July-2011
Text Book:
1. Fuzzy Sets and Fuzzy Logic-Theory and Applications by George J. Klir and Bo yuan, Prentice- Hall of India Private Limited, 2012. Unit I: Chapter 1,2: Sec 1.1-1.4, 2.1-2.3 Unit II: Chapter 3: Sec 3.1-3.5 Unit III: Chapter 4: Sec 4.1-4.4 Unit IV: Chapter 5: Sec 5.3,5.5-5.8 Unit V:Chapter 6: Sec 6.1-6.5
