The problem of multicriteria optimization on a fuzzy set, which is specified by its membership function, is considered. A two-step approach is proposed to solve this problem. One consists in finding a compromise between the available criteria and the membership function. At the first stage, a new vector criterion is formed, which is obtained by adding a membership function to a set of initial criteria, and information about the importance of criteria in the form of information quanta for the Pareto set reduction is used. If the set obtained after such reduction is not appropriate as the final solution of the multicriteria optimization problem, then in the second stage we use scalarization, realizing the idea of goal programming.