Easy Way to Understand Fuzzy Inference - 2

As discussed on easy-way-to-understand-fuzzy-inference-1 in previous, fuzzification of Input Variable Angle (4°) provides 2 membership functions:

• zero = 0.2
• pos_small = 0.8

and Distance (12 m) provides 2 membership functions:

• medium = 0.9
• far = 0.1

Below is the fuzzification' results of input variables into IF-THEN rules:  
#18: IF Angle = zero (0.2) AND Distance = medium (0.9) THEN Power = zero

#19: IF Angle = pos_small (0.8) AND Distance = medium (0.9) THEN Power = pos_med

#23: IF Angle = zero (0.2) AND Distance = far (0.1) THEN Power = pos_med

#24: IF Angle = pos_small (0.8) AND Distance = far (0.1) THEN Power = pos_med

    

 
    {X AND Y } means a minimum value between X and Y as shown in Figure above, and

      #18: min{0.2, 0.9} = 0.2

      #19: min{0.8, 0.9} = 0.8

      #23: min{0.2, 0.1} = 0.1

      #24: min{0.8, 0.1} = 0.1

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:IF Angle = pos_small(0.8) AND Distance = far(0.1)THEN Power = pos_med(0.1)

Finally, 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. This theory is famous and named as MIN-MAX method. Basically there are some methods in Fuzzy Logic system, and we will not be going to discuss more detail about these methods. We suggest you to read books or papers on Fuzzy Logic for more detail discussion.

Let ask us if you are still fuzzy on this...


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