A new approach for the automatic generation of membership functions and rules of multi-variable fuzzy system

That the amount of work of extracting and modulating membership functions and rules expands startlingly with the increasing of the number of variables is presently the crux that influences the development of fuzzy system. This paper introduces a method in which the complicated input-output relationship is firstly decomposed into the accumulation of simple input-output relationships. For each variable, a set of membership functions that are appropriate for all simple input-output relationships are generated, and multiple sets of fuzzy rules that reflect its efficacy on every simple input-output relationship are also extracted. The fuzzy rules of the whole system are then generated based on these sets of fuzzy rules. It is proved simultaneous that the membership functions generated by an individual variable appropriate for each simple input-output relationship are those of the whole system. Because the complicated problem is decomposed into the accumulation of simple ones, the complexity of its solution will not expand startlingly with the increasing of the number of variables and the algorithm can be put into practice.