A problem of multicriteria optimization on a fuzzy set specified by its membership function is considered. A two-step approach is proposed to solve this problem. It involves searching for a compromise between the available criteria and the membership function. At the first stage, a new vector criterion is formed by adding the membership function to the set of initial criteria and information about the importance of criteria in the form of quanta of information is used to reduce the Pareto set. If the reduced Pareto set is not chosen as the final solution to the multicriteria optimization problem, scalarization that uses the concept of ​​goal programming is proposed at the second stage.