Abstract
In a random fuzzy information system, by introducing a fuzzy t-similarity relation on the objects set for a subset of attributes set, the approximate representations of knowledge are established. By discussing fuzzy belief measures and fuzzy plausibility measures defined by the lower approximation and the upper approximation in a random fuzzy approximation space, some equivalent conditions of knowledge reduction in a random fuzzy information system are proved. Similarly as in an information system, the fuzzy-set-valued attribute discernibility matrixes in a random fuzzy information system are constructed. Knowledge reduction is defined from the view of fuzzy belief measures and fuzzy plausibility measures and a heuristic knowledge reduction algorithm is proposed, and the time complexity of this algorithm is O(|U|2|A|). A running example illustrates the potential application of algorithm, and the experimental results on the data sets with numerical attributes show that the proposed method is effective.
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