Variations and Absolute Continuity of Set Functions on T_∞-tribe  

作　　者：王锋叶 张强 

机构地区：[1]School of Management and Economics,Beijing Institute of Technology [2]School of Science,Henan University of Science and Technology

出　　处：《Journal of Beijing Institute of Technology》2009年第3期375-378,共4页北京理工大学学报（英文版）

基　　金：Sponsored by the National Natural Science Foundation of China(70471063,70771010);Youth Foundation of Henan University of Science and Technology(2007QN051)

摘　　要：some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.

关 键 词：fuzzy measure absolute continuity inclusion variation disjoint variation triangular norms 

分 类 号：O159[理学—数学]