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A heuristic algorithm for reduction of knowledge in probabilistic decision table based on fuzzy entropy

Knowledge reduction is one of the important problems in rough sets theory. There are many types of knowledge reductions in the area of rough sets. In this paper, first, probabilistic rough set is characterized by a fuzzy set which is determined by the rough membership function. Then, we give the uncertainty measures in probabilistic rough set using fuzzy entropy of the fuzzy set. It is different from information-theoretic measures of uncertainty for rough set, by which we can analyze the significance of every condition attributes in a probabilistic decision table, and regard it as heuristic information in order to decrease search space. Based on these, a heuristic algorithm for reductions of condition attributes with respect to every elementary categories of decision attributes is proposed. To illustrate this algorithm, a running example is presented.