Lecture 4: Fuzzy Inference System
General definition: A computing framework based on the concepts of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning.
Interpretation: Specifically, it is a framework used to model and infer the behaviour of a system. There two important parts:
- Encoding knowledge as a set of if-then rules
- Predict the system behaviour using the encoded knowledge
The basic structure of FIS are as follows:
- Inputs
- Can be fuzzy or crisp
- Outputs
- Always almost fuzzy set
- Rule Base
- Number of fuzzy if-then rules, each describing local behavior mapping
- Reasoning Mechanism
Note on rule base
If a antecedent has two different consequences, then the rule base is considered to be inconsistent.
Reasoning Mechanism: Defuzzification
Extracting a crisp value from a fuzzy set. The method of interest for the course are as follow:
Centroid of Area (COA) or Centre of Gravity (COG)
$$Z_{COG} = \frac{\int_z \mu_A(z)zdz}{\int_z \mu_A(z)dz}$$ Where $z$ is represents the position on the bar and $\mu_A(z)$ represents the density.