Various Forms of Fuzzy Composition Operations

If A and B are two fuzzy sets and R is a fuzzy relation such that B equal A .R

then the various forms of fuzzy composition operations are as follow:

Max-Min Composition:-

Max-Product Composition:-

Min-Max Composition:-

Max-Max Composition:-

Min-Min Composition:-

Max-Average Composition:-

Sum-Product Composition:-

Where f is a logistic function like that of step, sigmoid, or linear.