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*Fuzzy Sets and Systems*

Volume 55, Number 1 (April 1993), Pages 43-50.

## Abstract

If *f:R*^{n}->R is continuous and monotonic in each
variable, and if *µ*_{i} is a fuzzy number on the
*i*^{th} coordinate, then the membership on *R*
induced by *f* and by the membership on *R*^{n} given
by
*µ(x)=min(µ*_{1}(x^{1}),...,µ_{n}(x^{n}))
can be evaluated by determining the membership at the endpoints of the
level cuts of each *µ*_{i}. Here more general conditions
are given for both the function *f* and the manner in which the
fuzzy numbers *µ*_{i} 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.