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The application of rough set theory in incomplete information systems is akey problem in practice since missing values almost always occur in knowledgeacquisition due to the error of data measuring, the limitation of datacollection, or the limitation of data comprehension, etc. An incompleteinformation system is mainly processed by compressing the indiscernibilityrelation. The existing rough set extension models based on tolerance orsymmetric similarity relations typically discard one relation among thereflexive, symmetric and transitive relations, especially the transitiverelation. In order to overcome the limitations of the current rough setextension models, we define a new relation called the positive transitiverelation and then propose a novel rough set extension model built upon which.The new model holds the merit of the existing rough set extension models whileavoids their limitations of discarding transitivity or symmetry. In comparisonto the existing extension models, the proposed model has a better performancein processing the incomplete information systems while substantially reducingthe computational complexity, taking into account the relation of tolerance andsimilarity of positive transitivity, and supplementing the related theories inaccordance to the intuitive classification of incomplete information. Insummary, the positive transitive relation can improve current theoreticalanalysis of incomplete information systems and the newly proposed extensionmodel is more suitable for processing incomplete information systems and has abroad application prospect.

Extension of Rough Set Based on Positive Transitive Relation