structure of fuzzy inference system

Structure Of Fuzzy Inference System
Fuzzy inference is the actual process of mapping from a given input to an output using fuzzy logic. Fuzzy logic starts with the concept of a fuzzy set. Fuzzy inference systems (FIS) are one of the most famous applications of fuzzy logic and fuzzy sets theory
1. Fuzzifier:
It is a transformation of input variables to linguistic ones. Transformation is realized by introduction of so called membership functions, which define both a range of value and a degree of membership.


Structure of fuzzy inference system.

2. Inference Engine:
An inference mechanism (also called an “inference engine” or “fuzzy inference” module), which emulates the expert’s decision making in interpreting and applying knowledge. There are three main fuzzy logic inference systems:
1. Mamdani type is used in this work that it has fuzzy outputs.
2. Sugeno type.
3. Tsukamoto type.
3. Defuzzifier:
It is converting process Fuzzy output to crisp value and represents converting decisions to actions. Defuzzification operates on the implied fuzzy sets produced by the inference mechanism and combine their effects to provide the "most certain "controller output. Defuzzification can be resulted using several known methods, some of these methods are the following:
1. Centroid method.
2. Middle of Max method.
3. First of Maxima method.
4. Last of Maxima method.
1- Centroid Of Area
Is the most popular one. Mathematically, this centre of gravity (COG) can be expressed as:

where ?A(z) is the aggregated output MF and z is the output quantity.
For discrete values, above equation can be put in the form:


where ?A (kz) are the k=1,2,…,n sampled values of the aggregated output membership function.
Example: compute crisp value in this method using the following figuare:



sol:

5.41 = ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Crisp output =

2- Middle Of Maxima)
In this defuzzification technique, the average output value is obtained, where z1 is the first value and z2 is the last value, where the output overall membership function, ? A (z), is maximum.

Example: compute crisp value in this method using the following figuare:



Sol:
z1 = 6 , z2 = 7

z = ـــــــــــــــــــ = 6.5

3- First Of Maxima:
In this defuzzification technique, the first value of the overall output membership function with maximum membership ?A (z) degree is taken. It should be noted that this is equal to z1 used in the MOM defuzzification method .

4- Last Of Maxima:
When this defuzzification technique, the last value of the overall output membership function with maximum membership ? A (z ) degree is taken. It should be noted that this is equal to 2 z used in the MOM defuzzification method.
In general, the defuzzification operations are time consuming and they are not easily subject to rigorous mathematical analysis.
Exercise:
Compute crisp value using FOM and LOM for previous figuares:

Next lecture spooler:
After knowledge of the structure of inference engine , in the next lecture , we shall know the last part whih is Knowledge Base.