Lebesgue measure of α-cuts approach for finding the height of the membership function

Abstract

The goal of this paper is to present a procedure for finding the height (the global maximum) of a membership function of a fuzzy set of Rn, even for non-continuous membership functions, using the Lebesgue measure of α-cuts. Randomizing the variable and approximating the corresponding function to α-cuts completes the procedure. An algorithm is given for finding the height of the membership function, which is applied to some characteristic examples. © 2000 Elsevier Science B.V. All rights reserved.