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

Endre Pap, Dušan Surla

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)341-350
Number of pages10
JournalFuzzy Sets and Systems
Volume111
Issue number3
Publication statusPublished - May 1 2000

Fingerprint

Membership functions
Lebesgue Measure
Membership Function
Fuzzy sets
Fuzzy Sets
Membership function

Keywords

  • α-level
  • Height
  • Lebesgue measure; lebesgue integral
  • Membership function

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Information Systems and Management
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Statistics and Probability

Cite this

Lebesgue measure of α-cuts approach for finding the height of the membership function. / Pap, Endre; Surla, Dušan.

In: Fuzzy Sets and Systems, Vol. 111, No. 3, 01.05.2000, p. 341-350.

Research output: Contribution to journalArticle

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