Approximating α-cuts with the vertex method

Kevin N. Otto, Andrew D. Lewis, Erik K. Antonsson*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

37 Citations (Scopus)

Abstract

If f:Rn → R is continuous and monotonic in each variable, 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.

Original languageEnglish
Pages (from-to)43-50
Number of pages8
JournalFuzzy Sets and Systems
Volume55
Issue number1
DOIs
Publication statusPublished - 9 Apr 1993
MoE publication typeA1 Journal article-refereed

Keywords

  • analysis
  • data analysis methods
  • engineering
  • Fuzzy numbers
  • multiple criteria evaluation
  • topology

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