In multicriteria decision making (MCDM) aggregation of the values of sealed criterion functions is one of the most important steps. Fuzzy integrals (e .g. the Choquet integral, the Sugeno integral) are superior mathematical tools for aggregation in comparison with the usual approaches. The common additive approach is based on the assumption that analyzing criteria are mutually independent. This assumption is not common in practice . Fuzzy integrals (FI) are in the focus of interest because they have the possibility of modeling : (a) interactions between criteria, and (b) the redundancy of information contained in criterion functions. Most of the known approaches of aggregation are only special cases of the fuzzy integral. The main practical problem in applying fuzzy integrals is fuzzy measures (FM) determination. In this paper we present a new approach for fuzzy measures determination in MCDM using the fuzzy integral. Using this approach, a decision maker (DM) can systematically explicate his relation to the relevant importance of criteria as well as to possible interactions between criteria (amplifying the effect) and/or the possible redundancy of information contained in different criteria (reducing the effect). We illustrate the new approach of fuzzy measures through an example.