On fuzzy correlations

Daniel Ramot, Ron Milo, Menahem Friedman, Abraham Kandel

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

A general framework for dealing with numerical measurements in an approximate, uncertain, or fuzzy environment is presented. A fuzzy measurement is defined. It possesses several unique properties, which arise from its physical nature and distinguish it from concepts such as the fuzzy number. These properties, which include the fuzzy correlation term and the fuzzy equality relation, follow directly from physical considerations. The introduction of the fuzzy correlation term provides a mathematical tool for representing any correlation relations, which may exist between different fuzzy measurements. The main function of the fuzzy correlation term is to eliminate, or filter out, measurement values that are unlikely, given other fuzzy measurements. Thus, using the fuzzy correlation term, the range of possible measurement values is limited by physical realities. The information represented by the fuzzy correlation term is shown to be of great value in providing a wider picture of reality than it is possible to obtain by simply considering individual fuzzy measurements. Arithmetic operations on fuzzy measurements and functions of fuzzy measurements are also discussed, leading to the derivation of the fuzzy Riemann integral and its applications.

Original languageEnglish
Pages (from-to)381-390
Number of pages10
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume31
Issue number3
DOIs
StatePublished - 1 Jun 2001
Externally publishedYes

Keywords

  • Fuzzy arithmetic
  • Fuzzy correlation term
  • Fuzzy equality
  • Fuzzy integral
  • Fuzzy measurements
  • Fuzzy numbers

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

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