Abstract
A knowledge base is a basic concept in rough set theory. Uncertainty measures are critical evaluation tools in machine learning fields. This article investigates relationships between knowledge bases and their uncertainty measures. Firstly, dependence and independence between knowledge bases are proposed, and are characterized by the inclusion degree. Secondly, knowledge distance between knowledge bases is studied. Thirdly, invariant and inverse invariant characteristics of knowledge bases under homomorphisms based on data compression are obtained. Fourthly, measuring uncertainty of knowledge bases is investigated, and an example is provided to illustrate the fact that knowledge granulation, rough entropy, knowledge entropy, and knowledge distance are neither invariant nor inverse invariant under homomorphisms based on data compression. Finally, a numerical experiment is provided to show features of the proposed measures for uncertainty of knowledge bases, and effectiveness analysis is conducted from the two aspects of dispersion and correlation. These results will be helpful for the establishment of a framework of granular computing in knowledge bases.
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