Original manuscript: 1992/08/24
If f:Rn→R is continuous and monotonic in each variable, and if μi is a fuzzy number on the ith coordinate, then the membership on R induced by f and by the membership on Rn given by μ(x)=min{μ1(x1),..., μn(xn)} can be evaluated by determining the membership at the endpoints of the level cuts of each μi. Here more general conditions are given for both the function f and the manner in which the fuzzy numbers {μi} are combined so that this simple method for computing induced membership may be used. In particular, a geometric condition is given so that the α-cuts computed when the fuzzy numbers are combined using min is an upper bound for the actual induced membership.