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On Possibilistic Correlation

Christer Carlsson, Robert Fullér, Péter Majlender, On Possibilistic Correlation. Fuzzy Sets and Systems 115(425-445), 2005.

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.

BibTeX entry:

@ARTICLE{jCaFuMa05a,
  title = {On Possibilistic Correlation},
  author = {Carlsson, Christer and Fullér, Robert and Majlender, Péter},
  journal = {Fuzzy Sets and Systems},
  volume = {115},
  number = {425-445},
  year = {2005},
}

Belongs to TUCS Research Unit(s): Other

Publication Forum rating of this publication: level 1

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