On possibilistic mean value and variance of fuzzy numbers

Christer Carlsson, R. Fullér

Research output: Contribution to journalArticle

534 Citations (Scopus)

Abstract

Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we define the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. We also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which are consistent with the extension principle. We also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.

Original languageEnglish
Pages (from-to)315-326
Number of pages12
JournalFuzzy Sets and Systems
Volume122
Issue number2
DOIs
Publication statusPublished - Sep 15 2001

Fingerprint

Fuzzy numbers
Mean Value
Distribution functions
Notation
Possibility Distribution
Extension Principle
Interval
Closed interval
Continuous Distributions
Probability Theory
Linear Combination
Distribution Function

Keywords

  • Fuzzy numbers
  • Possibility theory

ASJC Scopus subject areas

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

Cite this

On possibilistic mean value and variance of fuzzy numbers. / Carlsson, Christer; Fullér, R.

In: Fuzzy Sets and Systems, Vol. 122, No. 2, 15.09.2001, p. 315-326.

Research output: Contribution to journalArticle

Carlsson, Christer ; Fullér, R. / On possibilistic mean value and variance of fuzzy numbers. In: Fuzzy Sets and Systems. 2001 ; Vol. 122, No. 2. pp. 315-326.
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