id: 06049893
dt: j
an: 
au: Majlender, Péter
ti: A note on the convexity assumption of possibilistic correlation.
so: Appl. Math. Lett. 25, No. 4, 672-675 (2012).
py: 2012
pu: Elsevier Science Ltd. (Pergamon), Oxford
la: EN
cc: 62
ut: joint possibility distribution; possibilistic correlation coefficient
ci: 
li: doi:10.1016/j.aml.2011.08.023
ab: Summary: In 2005, Carlsson, Fullér and Majlender introduced a measure of
    possibilistic correlation of fuzzy numbers A and B by their joint
    possibility distributionC as an average degree of interaction between
    the $γ$-level sets of A and B as compared to their individual
    dispersions. They proved that this possibilistic correlation
    coefficient can never exceed 1 in absolute value, if all $γ$-level
    sets of the joint possibility distribution C are convex. In this
    communication, we shall formulate a special class of joint possibility
    distributions with non-convex $γ$-level sets, for which the
    correlation coefficient can take values outside the interval [-1,1]. In
    particular, this result will show that the assumption about the
    convexity of the level sets of C is essential for the possibilistic
    correlation to be bounded by the interval [-1,1].
rv: