Heuristic algorithms for finding distribution reducts in probabilistic
  rough set model
  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.
