Course

Unit-I

Fuzzy Sets: Crisp Sets- an Overview, Fuzzy Sets-Definition and Examples, α-Cuts and its Properties, Representations of Fuzzy Sets, Extension Principles of Fuzzy Sets, Operations on Fuzzy Sets-Fuzzy Complements, Fuzzy Intersections, Fuzzy Unions, Combinations of Operations, Aggregation Operations.

Unit-II

Fuzzy Arithmetic: Fuzzy Numbers, Arithmetic Operations on Intervals, Arithmetic Operations on Fuzzy Numbers.

Unit-III

Fuzzy Relations: Binary Fuzzy relations, Fuzzy Equivalence Relations, Fuzzy Compatibility Relations.

Unit-IV

Fuzzy Logic: Classical Logic, Multivalued Logic, Fuzzy Propositions, Fuzzy Quantifiers, Linguistic Hedges, Inference from Conditional Fuzzy Propositions, Conditional and Qualified Propositions and Quantified Propositions,.

Unit-V

Uncertainty-Based Information: Information and Uncertainty, Non Specificity of Crisp Sets – Non Specificity of Fuzzy Sets, Fuzziness of Fuzzy Sets, Uncertainty In Evidence Theory, Principles of Uncertainty.

Course Outcomes:
CO-1: Understand the basic concepts of Fuzzy sets
CO-2: Understand the concepts of arithmetci operations on fuzzy numbers. CO-3: Understand the concepts Fuzzy relations.
CO-4: Understand the concepts of Fuzzy logic.
CO-5: Understand the concepts of uncertainty and crisp sets.

1. George J. Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic- Theory and Applications, Prentice Hall of India, 1997.
2. Timothy J. Ross, Fuzzy Logic with Engineering Applications, McGraw Hill, 1997.
3. H.J. Zimmermann, Fuzzy Sets and its Applications, Allied publishers, 1991.