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

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 possibility distributions, (1-x-y), (1-x 2-y 2), \((1-{\sqrt{x}-\sqrt{y}})\) and (1-x 2-y) on the set {(x,y)\({\mathbb R}^2\)| x≥0,y≥0,x+y≤1}, 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.KeywordsFuzzy NumberJoint DistributionMarginal DistributionAutocorrelation CoefficientPossibility DistributionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.