Fuzzy Logic Toolbox

An Example: Two Lines

To see a specific example of a system with linear output membership functions, consider the one input one output system stored in sugeno1.fis.

• fismat = readfis('sugeno1');
  getfis(fismat,'output',1)
      Name = output
      NumMFs = 2
      MFLabels =
          line1
          line2
      Range = [0 1]
  

The output variable has two membership functions.

• getfis(fismat,'output',1,'mf',1)
      Name = line1
      Type = linear
      Params =
          -1    -1
  getfis(fismat,'output',1,'mf',2)
      Name = line2
      Type = linear
      Params =
          1    -1
  

Further, these membership functions are linear functions of the input variable. The membership function line1 is defined by the equation

• output = (-1)*input + (-1)

and the membership function line2 is defined by the equation

• output = (1)*input + (-1)

The input membership functions and rules define which of these output functions will be expressed and when.

• showrule(fismat)
  ans =
  1. If (input is low) then (output is line1) (1)
  2. If (input is high) then (output is line2) (1)
  

The function plotmf shows us that the membership function low generally refers to input values less than zero, while high refers to values greater than zero. The function gensurf shows how the overall fuzzy system output switches smoothly from the line called line1 to the line called line2.

• subplot(2,1,1), plotmf(fismat,'input',1)
  subplot(2,1,2),gensurf(fismat)
  
  
  
  

This is just one example of how a Sugeno-type system gives you the freedom to incorporate linear systems into your fuzzy systems. By extension, you could build a fuzzy system that switches between several optimal linear controllers as a highly nonlinear system moves around in its operating space.

Sugeno-Type Fuzzy Inference

Conclusion