In this paper, information entropy about logarithmic form is used to measure uncertainty of knowledge, and the correlation connection between information entropy, conditional information entropy, joint information entropy and mutual information entropy are analyzed. Correlation coefficient ρ (B, C) between two attribute subsets in random information systems and ρ (C/-B) for a conditional attributes set B relative to another condition attributes set C w.r.t. the decision attributes set D in random decision information systems are introduced. The properties of correlation coefficients are discussed, and some concepts about random information systems and random decision information systems, such as indispensable attributes, consistent attributes and core attributes, etc, are described by using correlation coefficients. Some new methods of attribute reduction are proposed by using correlation coefficients, the corresponding algorithms based on attribute correlation coefficient are given in random information systems and in random decision information systems, the listed examples and the experimental result show that the algorithms are effective.
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