A knowledge base is one basic notion in rough set theory. In a knowledge base, one can approximately describe target notions by using existing knowledge structures. This paper investigates invariant characteristics of knowledge structures in a knowledge base under homomorphisms and their uncertainty measures. First, partial dependence knowledge structures in the same knowledge base is proposed and the concept of knowledge structure bases is presented. Then, invariant and inverse invariant characteristics of knowledge structures in a knowledge base under homomorphisms are obtained. Next, measuring uncertainty of knowledge structures in the same knowledge base is investigated. Finally, two examples are employed to illustrate that knowledge granulation, rough entropy, knowledge entropy and knowledge amount of knowledge structures, and knowledge distance between knowledge structures are neither invariant nor inverse invariant under homomorphisms, and third example shows the feasibility of the proposed measures for uncertainty of knowledge structures in the same knowledge base. These results will be helpful for building a skeleton of granular computing in knowledge bases.
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