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Determining the membership functions

 

As described earlier, a fuzzy set is fully defined by its membership function. How best to determine the membership function is the first question that has to be tackled.

For most control applications the sets that will have to be defined are easily identifiable. For other applications they will have to be determined by knowledge acquisition from an expert or group of experts. Once the names of the fuzzy sets have been established, one must consider their associated membership functions.

The approach adopted for acquiring the shape of any particular membership function is often dependent on the application. For most fuzzy logic control problems the assumption is that the membership functions are linear - usually triangular in shape. So, typically as Fig 3 [6] shows the sets that describe various factors of importance in robot control and the issues to be determined are the parameters that define the triangles (The problem in [6] is that of a two robot configuration in a shared work space with fuzzy sets being used to assist in collision avoidance). These parameters are usually based on the control engineer's experience and/or are generated automatically (see 4.2). However for many other applications triangular membership functions are not appropriate as they do not represent accurately the linguistic terms being modelled and so will have to be elicited directly from the expert, by a `statistical' approach or by automatic generation of the shapes. The determination of can be categorised as either being manual or automatic. The thrust, and interest, of this research is towards considering how artificial intelligence techniques, in particular, can be deployed to assist in the development of fuzzy inferencing systems. However it is worthwhile to consider how more traditional (manual) approaches may be deployed.

  
Figure 3: Some typical fuzzy sets for robot control





next up previous contents
Next: Manual methods for Up: No Title Previous: Fuzzy Inferencing Systems



Bob John
Fri Oct 25 14:41:29 BST 1996