Journal article

APPROXIMATING ALPHA-CUTS WITH THE VERTEX METHOD

KN OTTO, AD LEWIS, EK ANTONSSON

FUZZY SETS AND SYSTEMS | ELSEVIER SCIENCE BV | Published : 1993

Abstract

If f:Rn → R is continuous and monotonic in eachvariable, and if μi is a fuzzy number on the ith coordinate, then the membership on R induced by f{hook} and by the membership onfRn given by μ(x) = min(μ1(x1), ..., μn(xn)) can be evaluated by determining the membership at the endpoints of the level cuts of each μi. Here more general conditions are given for both the function f{hook} and the manner in which the fuzzy numbers {μi} 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. © 1993.

University of Melbourne Researchers