APPROXIMATING ALPHA-CUTS WITH THE VERTEX METHOD

被引：29

作者：

OTTO, KN ^{[1
]}

LEWIS, AD ^{[1
]}

ANTONSSON, EK ^{[1
]}

机构：

[1] CALTECH,DIV ENGN & APPL SCI,ENGN DESIGN RES LAB,PASADENA,CA 91125

来源：

FUZZY SETS AND SYSTEMS | 1993年 / 55卷 / 01期

基金：

美国国家科学基金会;

关键词：

FUZZY NUMBERS; ANALYSIS; TOPOLOGY; DATA ANALYSIS METHODS; MULTIPLE CRITERIA EVALUATION; ENGINEERING;

D O I：

10.1016/0165-0114(93)90300-7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

If f:R(n) --> R is continuous and monotonic in each variable, and if mu(i) is a fuzzy number on the ith coordinate, then the membership on R induced by f and by the membership on R(n) given by mu(x) = min(mu1(x1),..., mu(n)(x(n)) can be evaluated by determining the membership at the endpoints of the level cuts of each mu(i). Here more general conditions are given for both the function f and the manner in which the fuzzy numbers {mu(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 alpha-cuts computed when the fuzzy numbers are combined using min is an upper bound for the actual induced membership.

引用

页码：43 / 50

页数：8

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