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The concepts of comparability and credibility of the symmetric similarity relations are proposed. This paper builds a dual-limited symmetric similarity relation and construct the rough set model based on the dual-limited symmetric similarity relation. Then, this paper determine the upper approximation set, and lower approximate set and the boundaries domain to improve the granularity and accuracy of knowledge in incomplete information system. The effectiveness and practicality of the rough set model based on the dual-limited symmetric similarity relations are verified from the two aspects of theoretical and practice. [ABSTRACT FROM PUBLISHER]

In this paper, the incomplete information system with both absent and missing unknown values is deeply studied. Through characteristic relation, the limitation of characteristic class is pointed out such that not any two elements in a characteristic class are mutually tolerant. The technique of maximal consistent blocks is introduced into characteristic class and then the concept of characteristic consistent block is proposed, the corresponding rough set is then constructed. Not only the basic properties about characteristic consistent blocks based rough set are discussed, but also the relationship between characteristic consistent blocks and characteristic relation based rough sets are analyzed. It is shown that by comparing with the characteristic relation, we can obtain greater lower approximation and smaller upper approximation if characteristic consistent block approach is employed. [ABSTRACT FROM PUBLISHER]

The notion of homomorphism is used as a tool to deal with attribute reduction in incomplete information systems. In this paper, we define a tolerance relation on the universe of discoures U, and the tolerance classes which are created by the tolerance relation can form a cover of U. Then a novel definition of consistent function is proposed, and some properties of incomplete information systems under homomorphism are discussed. Furthermore, we prove that the attribute reduction of the original system and its image system is equivalent to each other. And then a new and more convenient measure to handle the attribute reduction of the original incomplete information system is obtained. [ABSTRACT FROM PUBLISHER]

For the universality of incomplete information and superiority of rough set over dual-universes, we research rough set over dual-universes in incomplete information system. In this paper, we provide a general character function in incomplete information system. Then lower and upper approximation operators of rough set over dual-universes in incomplete information system are constructed utilizing general character function. Basic properties of rough set over dual-universes in incomplete information system are studied. Relations between rough set over dual-universes rough set over dual-universes in incomplete information system are discussed. Also, some numerical examples are presented to illustrate theses concepts. [ABSTRACT FROM PUBLISHER]