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粗糙集理论与证据理论都是处理不确定性问题最重要的工具.在粗糙集理论中利用划分来描述集合的上、下近似,从而获取知识的不确定性.而证据理论使用证据函数来表示知识的不确定性.本文在粗糙集与证据理论的体系结构基础上,分析了粗糙集与证据理论两者中合成质量函数的不同,并对粗糙集理论中由划分的交运算获取的质量函数与证据理论中由证据的正交和运算获取的质量函数之间的关系进行了研究.证明了在满足一定条件的划分中,由划分的交运算获取的质量函数与证据的正交和运算获取的质量函数对应相等的结论.从而进一步澄清了粗糙集中由划分获取的质量函数与证据的正交和运算所获取的质量函数之间的关系.
Rough set theory and evidence theory are both the most important tools to deal with the problem of uncertainty.Using partitioning to describe the upper and lower approximation of the set in rough set theory to obtain the uncertainty of knowledge.And evidence theory using evidence function The uncertainty of knowledge.Based on the architecture of rough set theory and evidence theory, this paper analyzes the difference of synthetic quality function between rough sets theory and evidence theory, and analyzes the quality function And the quality of evidence theory obtained by the orthogonality and operation of the relationship between the function was studied.It is proved that in the division of a certain condition, Which is equal to the corresponding result of the mass function, so as to further clarify the relationship between the quality function obtained by partitioning and the quality function obtained by the orthogonal function of the evidence and the obtained quality function.