Approximate Reasoning Based on Upper Approximation

In order to investigate the approximate information contained in upper approximation, a mathematical structure called a tree-approximate space is defined, which is an extension of an approximate space in rough set theory. By integrating upper approximation with a tree in the tree-approximate space, approximate reasoning is introduced. It establishes connections between vertices, and can determine whether a vertex approximately deduces another. Making researches on approximate reasoning, some properties are obtained, which show that approximate reasoning not only preserves the connections between vertices induced by accurate information, but also extends the connections. This indicates that the approximate information contained in upper approximation can be developed by a reasoning approach. Besides, as a mathematical structure, a tree-approximate space with approximate reasoning can be used to model practical problems.