On possibilistic correlation

Christer Carlsson, R. Fullér, Péter Majlender

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

In 2004, Fullér and Majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact. Based on this approach, in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to their respective dispersions. Moreover, we will formulate the classical Cauchy-Schwarz inequality in this possibilistic environment and show that the measure of possibilistic correlation satisfies the same property as its probabilistic counterpart. In particular, applying the idea of transforming level sets of possibility distributions into uniform probability distributions, we will point out a fundamental relationship between our proposed possibilistic approach and the classical probabilistic approach to measuring correlation.

Original languageEnglish
Pages (from-to)425-445
Number of pages21
JournalFuzzy Sets and Systems
Volume155
Issue number3
DOIs
Publication statusPublished - Nov 1 2005

Fingerprint

Possibility Distribution
Dispersions
Probability distributions
Joint Distribution
Cauchy-Schwarz inequality
Probabilistic Approach
Marginal Distribution
Fuzzy numbers
Uniform distribution
Level Set
Probability Distribution
Interaction
Joint distribution

Keywords

  • Cauchy-Schwarz inequality
  • Covariance
  • Possibility distributions
  • Probability distributions
  • Variance

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 correlation. / Carlsson, Christer; Fullér, R.; Majlender, Péter.

In: Fuzzy Sets and Systems, Vol. 155, No. 3, 01.11.2005, p. 425-445.

Research output: Contribution to journalArticle

Carlsson, C, Fullér, R & Majlender, P 2005, 'On possibilistic correlation', Fuzzy Sets and Systems, vol. 155, no. 3, pp. 425-445. https://doi.org/10.1016/j.fss.2005.04.014
Carlsson, Christer ; Fullér, R. ; Majlender, Péter. / On possibilistic correlation. In: Fuzzy Sets and Systems. 2005 ; Vol. 155, No. 3. pp. 425-445.
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