Abstract One aspect that is often disregarded in the current research on evolutionary multiobjective optimization is the fact that the solution of a multiobjective optimization problem involves not only the search itself, but also a decision making process. Most current approaches concentrate on adapting an evolutionary algorithm to generate the Pareto frontier. In this work, we present a new idea to incorporate preferences into a multi-objective evolutionary algorithm (MOEA). We introduce a binary fuzzy preference relation that expresses the degree of truth of the predicate “ x is at least as good as y ”. On this basis, a strict preference relation with a reasonably high degree of credibility can be established on any population. An alternative x is not strictly outranked if and only if there does not exist an alternative y which is strictly preferred to x . It is easy to prove that the best solution is not strictly outranked. For validating our proposed approach, we used the non-dominated sorting genetic algorithm II (NSGA-II), but replacing Pareto dominance by the above non-outranked concept. So, we search for the non-strictly outranked frontier that is a subset of the Pareto frontier. In several instances of a nine-objective knapsack problem our proposal clearly outperforms the standard NSGA-II, achieving non-outranked solutions which are in an obviously privileged zone of the Pareto frontier.