Is there any restrictions in the number of membership functions of FLC?
Is it must to have all the output MFs related with rule base if we have more than what we need?
Say I have 2 input variables with 4 subsets each which results in 16 rules. I have selected 40 membership functions in the output with very small values and amongst them only 12 are related to my rule base. Other 28 M.Fs lies between the range.. Can I implement a FLC like that?
Membership functions are usually decided based upon the users requirement, though there is no restriction upon the number of membership functions.
Increasing the number of membership functions increasing the rule base table dimension and the system will be slow
Dear Sheik Mohammed.
There are no restrictions on the number of membership functions you can use in your FLC, however, think about how the FLC works and what it is used for.
When you think about how it works: When you have 28 (output) membership functions not represented in the rule base, it means your FLC will not produce any of them in the fuzzy output. However, after defuzzification, you can still get a crisp value which has a high membership degree in one (or more) of the 28 membership functions than in the ones used in the rule-base (subject to the defuzzification you choose). As an example, imagine your rule-base contains the outputs "high" and "low", but your output membership functions are "high", "medium" and "low". It's easy to imagine that defuzzifying an output of equal "high" and "low" may give a crisp value which is better fit for the set "medium".
When you think about what it is used for: Granular computing, where you can use the number of membership functions to increase or decrease the "precision" of your FLC. I.e. you control how how well the FLC can approximate the underlying function. More membership functions makes the system less "human" friendly, but more "precise".
I would consider if all 40 output membership functions are needed, or, if you can reconstruct them, so you only use the ones in the rule-base. More information about the problem you're trying to solve with a FLC could give more insight into whether it's a good suggestion or not.
Best regards.
Yes, there is no restriction regarding the no. of MFs. But the case that you mentioned is not a good FLC, because when we design a FLC, we consider only those MFs for output parameter which we desire for our context. Now, if any MF of output parameter is absent in the consequent part of fuzzy if-then rules throughout the whole rule-base, then it implies that in our context, there will be no such situation where I have to correspond our output to that particular MF. Thus, there is no need for that particular MF to consider for our output parameter at all.
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