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The basic concepts of Pawlak rough function model are improved. The concepts of double approximation operators that are scale upper (lower) approximation and real line upper (lower) approximation are defined and their properties and antithesis characteristics are analyzed. Scale bijection theorem as well as relative propositions and conclusions are proposed(More)
Many kinds of reducts are proposed in incomplete or inconsistent ordered information systems in recent years. But some of these reducts are equivalent. In this paper, we prove that the reduct preserving compatible (possible) distribution functions is equivalent to the reducts preserving lower (upper) approximations and give a more simple method to compute(More)
In an Ordered Decision Information System (ODIS), upper (lower) consistent objects are considered, and used to cope with inconsistency of the system and draw " at least " (" at most ") decision rules. The upper (lower) consistent objects are described by generalized decisions of the objects, and thereby generalized conveniently to the Ordered Decision(More)