In our paper we study the usage of partially defined Boolean functions (PDBFs) for generating cryptographically strong Boolean functions. A PDBF can be considered as a Boolean function with some undefined (unknown) values, i.e. its values are from the set 0,1,?. We generalize certain cryptographic properties to PDBFs, such as balancedness, nonlinearity and propagation characteristics. It is shown that usual relationships among properties hold for these generalizations as well. We apply these results to methods for generating cryptographically strong Boolean functions. We focus on greedy approach and test it in various settings. The paper compares obtained results with other methods.