Easy Way to Understand Defuzzification Method

As explained in the previous discussion, defuzzification is a process to convert linguistic values (Fuzzy values) into numerical values (real values). There are some methods of defuzzification technique:

1. Maximum Defuzzification Method
  

    

  

 
2. Centroid Defuzzification Method (Center of Maximum Method)

3. Weighted Average Defuzzification Method

Where,

• x* is the defuzzified output, 
• µi(x) is the aggregated membership function and 
• x is the output variable. 
• mi is the membership of the output of each rule, and  
• wi is the weight associated with each rule.

We will not be going to discuss more detail about these techniques, and we suggest you to read books or papers on Fuzzy Logic for more detail discussion of this topic.

As discussed in previous discussion, Fuzzy Inference results of the system are;

• #18:IF Angle = zero (0.2) AND Distance = medium (0.9) THEN Power = zero (0.2)
• #19:IF Angle = pos_small (0.8) AND Distance = medium (0.9) THEN Power = pos_med (0.8)
• #23:IF Angle= zero (0.2) AND Distance = far (0.1) THEN Power = pos_med (0.1)
• #24:IFAngle= pos_small (0.8) AND Distance = far (0.1) THEN Power= pos_med (0.1)

Result for the Linguistic Variable “Power” are:

                   zero with the degree 0.2

                   pos_med with the degree 0.8 and 0.1

Since pos_med has 2 values, select the maximum of the values i.e. 0.8 (MIN-MAX theory).
                  
Finally, result for the Linguistic Variable “Power” are:
                   zero with the degree 0.2

                   pos_med with the degree 0.8 

Locate linguistic variables of Power 0.2 & 0.8 (Y axis) at membership function of output; 0.2 at zero and 0.8 at pos_medium as shown in figure below.

In this discussion we will use Center of Maximum method for the defuzzification therefore the real value of Power will be 6.4 K Watt. 

Let us try to calculate the defuzzification result using Weighted Average Defuzzification method as follow;

x* = ((0.2*(-17.5) + (0.2*7.5) + (0.8*7.5) + (0.8*10)) / (0.2 + 0.2 + 0.8 + 0.8) 
    
     = 7 K Watt

There is different result of defuzzification depending the method used. An expert engineer has better knowledge and experience of the system will be controlled.







Source of figures: Industrial Application of Fuzzy Logic Control (slide presentations), Inform Software Corporation, 20001 Midwest Rd., Oak Brook, IL 60521, U. S. A.