Rough set theory is an effective mathematical?tool to deal with inaccuracy, uncertainty, and incompleteness of knowledge. Note that the classical rough set theory is based on complete information systems. However, incomplete information systems are frequently encountered in the real world. As a result, extension of rough set model and attribute reduction are basic issues for incomplete ordered information systems. For the incomplete ordered information systems with missing unknown attribute values, both the generalized extended dominance relation and limited extended dominance relation are not able to compare the dominance relationship of two objects. Motivated by this problem,-dominance relation was proposed based on the probability distributions of attribute values. And then, we put forward the notion of -dominance-relation-based relative reducts and their implementation method from the perspective of matrix. Furthermore, a real example was used to show the validity and advantages of -dominance relation. Finally, we carry on the simulation experiments on UCI data sets, simulation experiments were made to illustrate that more reasonable approximation accuracy can be obtained using -dominance relation of the incomplete ordered information system. athematicalmethodAnd carries on the simulation experiments on UCI data sets, the experiment illustrate the advantages of in for the superiority of attribute reduction
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Footnotes
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