  Possibilistic risk theory starts from the hypothesis that risk is modelled by
fuzzy numbers. In particular, in a possibilistic portfolio choice problem, the
return of a risky asset will be a fuzzy number. The expected utility operators
have been introduced in a previous paper to build an abstract theory of
possibilistic risk aversion. To each expected utility operator one can
associate a notion of possibilistic expected utility. Using this notion, we
will formulate in this very general context a possibilistic choice problem. The
main results of the paper are two approximate calculation formulas for
corresponding optimization problem. The first formula approximates the optimal
allocation with respect to risk aversion and investor's prudence, as well as
the first three possibilistic moments. Besides these parameters, in the second
formula the temperance index of the utility function and the fourth
possibilistic moment appear.
