## Tuesday, November 30, 2010

### Fuzzy Inferencing

Fuzzy Inferencing

The process of fuzzy reasoning is incorporated into what is called a Fuzzy Inferencing System. It is comprised of three steps that process the system inputs to the appropriate system outputs. These steps are 1) Fuzzification, 2) Rule Evaluation, and 3) Defuzzification. The system is illustrated in the following figure.

1Fuzzification

is the first step in the fuzzy inferencing process. This involves a domain formation where crisp inputs are transformed into fuzzy inputs. Crisp inputs are exact inputs measured by sensors and passed into the control system for processing, such as temperature, pressure, rpm's, etc.. Each crisp input that is to be processed by the FIU has its own group of membership functions or sets to which they are transformed. This group of membership functions exists within a universe of discourse that holds all relevant values that the crisp input can possess. The following shows the structure of membership functions within a universe of discourse for a crisp input.

2 Degree of membership:

degree to which a crisp value is compatible to a membership function, value from 0 to 1, also known as truth value or fuzzy input.membership function, MF: defines a fuzzy set by mapping crisp values from its domain to the sets associated degree of membership.

3.crisp inputs: distinct or exact inputs to a certain system variable, usually measured

4.parameters external from the control system, e.g. 6 Volts.

5.label: descriptive name used to identify a membership function.

6.scope: or domain, the width of the membership function, the range of concepts, usually numbers, over which a membership function is mapped.

7.universe of discourse: range of all possible values, or concepts, applicable to a system variable. When designing the number of membership functions for an input variable, labels must initially be determined for the membership functions. The number of labels correspond to the number of regions that the universe should be divided, such that each label describes a region of behavior. A scope must be assigned to each membership function that numerically identifies the range of input values that correspond to a label. The shape of the membership function should be representative of the variable. However this shape is also restricted by the computing resources available. Complicated shapes require more complex descriptive equations or large lookup tables. The next figure shows examples of possible shapes for membership functions.