Fuzzy Basics and Fuzzy Inference
It’s quite warm today When the road is slippery, drive slower
I am going to toss a coin. (Toss) Who thinks it
is a head?
Probability(head) = ? Let’s check. Now who thinks it is a head?
Who thinks it will rain tomorrow? What is the forecast? What will you answer next week?
This coin contains nickel Nickel is a metal Metals conduct electricity
Give me three examples of each…
Fuzzy Logic & Fuzzy Sets
(a) Boolean Logic.
(b) Multi-valued Logic.
(x) X Fuzzy S ubset A 1
0 Crisp S ubset A Fuzziness Fuzziness
Fuzzy sets example
See FuzzySets.xls A small FuzzySet program - FuzzyExample
A Fuzzy assertion
It is quite cold today Fuzzy variable – temperature Fuzzy set – cold temperatures More examples about height, sportiness,
Add to FuzzyExample
Complement Containment Intersection Union Draw diagrams
A Fuzzy rule
Very tall, sporty people are slim. Add this to the FuzzyExample program
Fuzzy inference (Text p106)
Rule: 1 IF project_funding is adequate OR project_staffing is small THEN risk is low Rule: 2 IF project_funding is marginal AND project_staffing is large THEN risk is normal Rule: 3 IF project_funding is inadequate THEN risk is high
Fuzzy inference steps
1. 2. 3. 4.
Fuzzification Rule evaluation Aggregation Defuzzification
Mamdani or Sugeno – style Change example to Sugeno -style