Fuzzy Sets and Systems
Volume 55, Number 1 (April 1993), Pages 43-50.
Abstract
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 alpha-cuts computed when the
fuzzy numbers are combined using min is an upper bound for the actual
induced membership.