I am very new to fuzzy logic. And I read a lot of examples over the internet. But I could not understand one particular example where only non overlapping member fuctions were used (which I find very uncommon). So I would like to have a better understanding in this aspect.
and one more request.
I am trying the implemetation for fuzzy controller in C. So if there is any good material to read I would appreciate if you can suggest.
Thank You
Fuzzy sets has to overlap. As such, overlapping denotes uncertainty in participation of members of the set to a particular set. If they do not overlap, the members do not carry any uncertainty. It is fundamental that an element of a fuzzy set is also an element of some other fuzzy set with some degree of belongingness.
When the membership functions of a fuzzy controller have oveelap, then we obtain an smooth and continous control signal near the boundaries of the membership functions. For example, consider two triangular membership functions without any overlap which stand for low and high control input. When the high membership function is activated, you have a high control input. When the high membership function switches with the that of low, the control input sudenly (discontinuesly) switches to small control input.
Membership function (MF) defines a class, e.g. winter (days), spring, summer, automm. In the real world spring does not go suddenly in summer as in calendar. Transformation of spring in summer occurs continuoesly and stepwise.
If you are using only one fuzzy set for whole universe of discourse, then there is no question of overlapping because you are denying the possibility of existence of more than one fuzzy set. If you are using two fuzzy sets e.g. person of age 5-10 (Child) 15-20 (adult), again there is no question of overlapping. But if you are using three fuzzy sets 5-10 (Child), 10-15 (Young) and 15-20 (adult), there there must overlapping to deal that age of few persons that may belong to both child as well as yong. And young as well as adult.
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