In this paper, incomplete fuzzy information system is studied. In order to deal with it by rough set theory, fuzzy compatible relation and fuzzy rough approximation are defined by logic function. Furthermore, fuzzy covering on universe is proposed, three different operations on the coverings are formed and then some significant results are gained. Besides, with the two new definitions of fuzzy rough entropies, uncertain factors could be effectively measured, some important relationships between the varieties of uncertain factors and the strength of those entropies are discussed carefully. Finally, knowledge dependency in rough set theory is transformed to fuzzy knowledge dependency in the incomplete fuzzy information system. A new method for measuring the strength of partial fuzzy knowledge dependency is proposed. Some immediate theorems are proved.