**Original manuscript:** 1992/08/24

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 α-cuts computed when the fuzzy numbers
are combined using min is an upper bound for the actual induced membership.

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