Fuzzy Sets and Systems
Volume 60, Number 1 (November 1993), Pages 19-24.
Consider sets X and Y each with associated
membership functions. Further suppose that there is a map
f:X -> Y.
A membership may be induced on Y from the membership on X
calculated using the extension principle, and the two
memberships on Y may be combined to give an overall
membership. The point with the highest membership in X
can be determined
directly or by back mapping the value with the highest membership in Y.
These two methods are equivalent under hypotheses on the
membership functions and on f. An example calculation from
engineering design is presented.