Material Covered in Lecture #2

Recap of Lecturse #1a &and #1b

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

Material Covered in Lecture #3

Recap of Lecture #2

Generalized Modus Ponens

1. Numerical Example
2. Three possible implementations of Modus Ponens
3. Computational Issues
   • Storage Complexity
   • Debugging with lambda values
   • Performance (proportion of active rules)

Extension Principle

1. Extension Principle: Theory and Implementation
2. Representation: Discrete (Sampling) and Parametrized
3. Fuzzy numbers
4. Interval and fuzzy arithmetics
5. Table of Close-formed Formulae for convex normal fuzzy numbers
   • Conditions of applicability
   • Assumptions for closure
6. Algebraic properties of positive normal convex fuzzy numbers (commutative semi-ring)

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