知识测度  

Knowledge Measure

作　　者：张贤勇[1] 莫智文[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2004年第2期152-154,共3页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金 (6980 3 0 0 7);四川省青年科学基金资助项目

摘　　要：在知识库中引入勒贝格测度 ,定义了知识测度和知识可测 ,对比勒贝格测度研究了知识测度的性质 ,并得出了波雷耳集与知识可测集等价等强于勒贝格测度的性质 .证明了知识外内测度刚好是知识上下近似的体积 ,知识可测与知识可定义等价的测度与粗糙集的深刻联系 ,并由此研究了知识精细关系下近似集与知识测度的性质 .Lebesgue measure is introduced in knowledge base, knowledge measure and knowledge measurable sets are defined. In contrast to Lebesgue measure, the properties of knowledge measure are studied, and some more powerful properties are achieved, such as Borel set is equal to knowledge measurable set. The deep connection between measure and rough sets is discovered. For example it is proved that knowledge outer and inner measures are just the volumes of upper and lower approximations, and that knowledge measurable set is equal to knowledge definable set. The properties of approximations and knowledge measure for finer on knowledge are also studied.

关 键 词：粗糙集 勒贝格测度 知识测度 波雷耳集 

分 类 号：O174[理学—数学] TP18[理学—基础数学]