1. Developed by Joseph GoguenJoseph Goguen

2. What is fuzzy sets Definition

3. Operations A={(x1,0.5),(x2,0.7),(x3,0)} B={(x1,0.8),(x2,0.2),(x3,1)} Union Intersection Complement Product of two fuzzy sets Equality Product of a fuzzy set with a crisp no. Power of a fuzzy set Difference Disjunctive sum

4. Properties Commutativity Associativity Distributivity Idempotence Identity Transitivity

5. Fuzzy Reasoning Many decision-making task are too complex to be understood quantitatively, however, humans succeed by using knowledge that is imprecise rather than precise. Fuzzy logic resembles human reasoning in its use of imprecise information to generate decisions. fuzzy logic incorporates an alternative way of thinking, which allows modeling complex systems using a higher level of abstraction originating from our knowledge and experience. Fuzzy logic allows expressing this knowledge with subjective concepts such as very big and a long time which are mapped into exact numeric ranges. Fuzzy logic provides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems

6. Example of Inference rules Every soldier is strong-willed. All who are strong-willed and sincere will succeed in their career. Indira is a soldier. Indira is Sincere. Solution: For all x (soldier(x) -> strong-willed(x)) For all x ((strong-willed(x) ^sincere(x)) -> succeed_career(x)) Soldier(indira) Sincere(indira)