Attribute reduction is one of the most important topics in rough set theory. Heuristic attribute reduction algorithms have been presented to solve the attribute reduction problem. It is generally known that fitness functions play a key role in developing heuristic attribute reduction algorithms. The monotonicity of fitness functions can guarantee the validity of heuristic attribute reduction algorithms. In probabilistic rough set model, distribution reducts can ensure the decision rules derived from the reducts are compatible with those derived from the original decision table. However, there are few studies on developing heuristic attribute reduction algorithms for finding distribution reducts. This is partly due to the fact that there are no monotonic fitness functions that are used to design heuristic attribute reduction algorithms in probabilistic rough set model. The main objective of this paper is to develop heuristic attribute reduction algorithms for finding distribution reducts in probabilistic rough set model. For one thing, two monotonic fitness functions are constructed, from which equivalence definitions of distribution reducts can be obtained. For another, two modified monotonic fitness functions are proposed to evaluate the significance of attributes more effectively. On this basis, two heuristic attribute reduction algorithms for finding distribution reducts are developed based on addition-deletion method and deletion method. In particular, the monotonicity of fitness functions guarantees the rationality of the proposed heuristic attribute reduction algorithms. Results of experimental analysis are included to quantify the effectiveness of the proposed fitness functions and distribution reducts.
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