Modelling Non-Linear Rendering Processes - Real-Time Rendering: Computer Graphics with Control Engineering - page 54

Knowledge Base

Database Rule base

Output

Input

Fuzzification Defuzzification

Decision making

FIGURE 4.3 (See colour insert.) Fuzzy inference system.

In general, a fuzzy inference system (Figure 4.3) consists of five functional com-
ponents:

1. A fuzzification process that transforms discrete values (inputs) into various
degrees of membership with linguistic values

2. A rule base containing a set of fuzzy if-then rules

3. A set of membership functions of the fuzzy sets used in the rule base

4. A decision-making process that performs fuzzy inference operations on
the rules

5. A defuzzification process that maps fuzzy results from the inference engine
to a crisp output

The process for fuzzy reasoning performed by a fuzzy inference system is as follows.

1. Fuzzify the input values by comparing the input variable with the member-
ship function to obtain their corresponding membership values.

2. Combine the membership values of all the premise components to find the
firing strength of each rule.

3. Generate the consequent results from each rule depending on the firing
strength.

4. Defuzzify the results by aggregating the qualified consequents to produce
the final crisp value.

The development of a fuzzy control system begins with the two key components:
(1) the input-output membership functions describing the properties of the system
(fuzzy sets) based on linguistic variables and (2) the rule-base that relates the
input-output sets. Given an antecedent and consequent relationship between an
input y to a SISO system's output u using linguistic descriptions of their properties,
the calculation may be represented as

IF yYTHEN uU
j

∈ ∈ (4.1)

j