Title: Determining optimal points of membership with dependent variables
Author(s): Kevin N. Otto, Andrew D. Lewis, and Erik K. Antonsson
Detail: Fuzzy Sets and Systems 60(1), pages 19-24, 1993
Journal version: Download

Original manuscript: 1993/03/14

Consider sets X and Y each with associated membership functions. Further suppose that there is a map f:XY. A membership may be induced on Y from the membership of 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.

No online version avaliable.

Andrew D. Lewis (andrew at mast.queensu.ca)