Material Covered in Lecture #2

Recap of Lecture #1

Fuzzy Logic Theory: Basic Concepts

1. Definition of a fuzzy set
2. Membership (characteristic) function
3. Set operations (union, intersection, complementation)
4. Algebraic Properties (Idempotency, Distributivity, Excluded Middle, etc.)
5. T-norms Overview (DeMorgan Law for T-norms and T-Conorms)
6. Level Sets (Alpha cuts, Core, Support, Bandwidth, Identitity Principle)
7. Possibilistic interpretation
8. Cardinality of a Fuzzy set
9. Measure of fuzziness of a fuzzy sets (entropy)
10. Numerical example

Fuzziness vs. Probability

1. Interpretations and Differences
2. Inference Mechanism: Modus Ponens vs.Conditioning
3. Possibility Measure

Approximate Reasoning

1. Fuzzy relations
2. Fuzzy Composition
3. Geometric and algebraic representation of Modus Ponens
4. Implementational issues

Homework Set 0

TBD

PDF Files of Slides for Lectures 2 and 3

Author: Piero P. Bonissone bonissone@crd.ge.com