On inference structures for fuzzy systems modeling

Fuzzy systems modeling involves the use of a fuzzy rule base to model complex systems by partitioning the input space into fuzzy regions in which the output can be more effectively represented. Typical of these situations are set of n rules of the form: if V is A_i then U is B_i where A_i and B_i are fuzzy subsets of the input and output spaces X and Y. The problem of finding the value of the output variable U given a value for the input variable V is called the fuzzy model inference or reasoning process. This process consists of the following four step algorithm: 1) determination of the relevance or matching of each rule to the current input value; 2) determination of the individual output of each rule; 3) aggregation of the individual rule outputs to obtain the overall fuzzy output; and 4) selection of some action based upon the output fuzzy set. Our purpose here is to describe the class of operators appropriate for the implementation of the rule output aggregation. Because of the strong interrelationship between all the steps in the process, we look at all the steps