广义拟Sugeno积分的次可加性和自连续性  

The subadditivity and autocontinuity of the generalized quasi Sugeno integral

作　　者：李艳红[1] LI Yanhong(Department of Mathematics,Teacher’s College,Easten Liaoning University,Dandong 118003,Liaoning Province,China)

机构地区：[1]辽东学院师范学院数学系

出　　处：《浙江大学学报（理学版）》2020年第1期67-71,100,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(61374009);辽东学院科研基金重点项目(2017ZD009)

摘　　要：广义拟Sugeno积分是基于诱导算子和经典Sugeno模糊积分建立的新型非可加积分,是对传统Sugeno模糊积分的推广,具有独特的积分性质和理论价值。在K-拟加测度空间上通过诱导算子引入广义拟Sugeno积分定义,并将该积分看作集函数,证明该集函数对任意2个可测集和拟加法满足次可加性。依这种特定集函数的次可加性,获得了广义拟Sugeno积分的上(下)自连续性和零可加(减)性,进而阐述该积分的自连续和零可加(减)的蕴含关系。A generalized quasi Sugeno integral is a new non-additive integral established based on the induction operator and the classical Sugeno fuzzy integral,it is not only a generalization of the traditional Sugeno fuzzy integral,but also has unique integral properties and theoretical value.In this paper,the definition of a generalized quasi Sugeno integral is introduced through an induction operator,and taking the integral as a set function,it is proved that the set function satisfies the subadditivity for the pseudo addition.The upper(lower)autocontinuity and zero additivity(subtractive property)of the generalized quasi Sugeno integral are discussed according to the subadditivity of the specific set function.Furthermore,the implication relation between the autocontinuity and zero additivity of the integral is expounded.

关 键 词：诱导算子 广义拟加Sugeno积分 次可加 自连续 零可加 

分 类 号：O159[理学—数学]