## Some Examples of Computing the Possibilistic Correlation Coefficient from Joint Possibility Distributions

Robert Fullér, József Mezei, Péter Várlaki, Some Examples of Computing the Possibilistic Correlation Coefficient from Joint Possibility Distributions. In: Imre J. Rudas, János Fodor, Janusz Kacprzyk (Eds.), Computational Intelligence in Engineering, Studies in Computational Intelligence Series, Studies in Computational Intelligence 313, 153–169, Springer, 2010.

http://dx.doi.org/10.1007/978-3-642-15220-7_13

### Abstract:

In this paper we will show some examples for computing the possibilistic correlation coefficient between marginal distributions of a joint possibility distribution. First we consider joint possibillity distributions, $(1-x-y)$, $(1-x^2-y^2)$, $(1-\sqrt{x}-\sqrt{y})$ and $(1-x^2-y)$ on the set $\left\lbrace (x,y) \in \mathbb{R}^{2} \mid x \geq 0, y \geq 0, x+y \leq 1 \right\rbrace$ then we will show (i) how the possibilistic correlation coefficient of two linear marginal possibility distributions changes from zero to -1/2, and from -1/2 to -3/5 by taking out bigger and bigger parts from the level sets of a their joint possibility distribution; (ii) how to compute the autocorrelation coefficient of fuzzy time series with linear fuzzy data.

### BibTeX entry:

@INBOOK{cFuMeVa10a,  title = {Some Examples of Computing the Possibilistic Correlation Coefficient from Joint Possibility Distributions},  booktitle = {Computational Intelligence in Engineering, Studies in Computational Intelligence Series},  author = {Fullér, Robert and Mezei, József and Várlaki, Péter},  volume = {313},  series = {Studies in Computational Intelligence},  editor = {Rudas, Imre J. and Fodor, János and Kacprzyk, Janusz},  publisher = {Springer},  pages = {153–169},  year = {2010},  keywords = {Correlation coefficient, autocorrelation},}

Belongs to TUCS Research Unit(s): Institute for Advanced Management Systems Research (IAMSR)

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