A note on \(f\)-weighted possibilistic correlation for identical marginal possibility distributions (Q533139)

In a recent paper, \textit{R. Fullér, J. Mezei} and \textit{P. Várlaki} [Fuzzy Sets Syst. 165, No. 1, 50--60 (2011; Zbl 1220.94068)] have defined possibilistic correlation between fuzzy numbers. There was a guess that for identical nonsymmetrical marginal possibility distributions \(A(x) = 1-x\) for all \(x\) from the unit interval one cannot find any joint possibility distribution and any \(f\)-weighting function for which the possibilistic correlation could go below \(-3/4\). In this note the author presents an example where the possibilistic correlation under the above side conditions tends to \(-1\).