一种非可加测度上的拟积概率积分研究  

A Probabilistic Integral Study of Quasi-product Over a Non-additive Measure

作　　者：赵辉 张小雪 张绍鑫 ZHAO Hui;ZHANG Xiao-xue;ZHANG Shao-xin(School of Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2021年第6期131-137,共7页Journal of Harbin University of Science and Technology

基　　金：四川省科技计划项目(2016JZ0014-1);黑龙江省自然科学基金(A201214).

摘　　要：给出了一种非可加测度的定义,其具有F可加性;并对Einstein算子进行了优化,设计了λ模糊拟积算子和λ模糊拟和算子,证明其满足T范数与S范数的条件;接下来基于这种非可加测度和模糊拟积算子给出了模糊拟积概率积分的定义,并将其积分整体看成一个集函数,研究并证明其满足的性质,由此丰富了模糊测度的理论。In this paper,a definition of non-additive measure is given,which has F-addability;the Einstein calculater is optimized,and theλ-fuzzy quasi-product operator andλ-fuzzy quasi-sum operator with adjustable parameters for practical problems are designed,and it is proved that they satisfy the conditions of T-norm and S-norm;then,based on this non-additive measure andλ-fuzzy quasi-product operator,the definition of fuzzy quasi-product probability integral is given,and the integral as a whole is regarded as a set function,and the nature of its satisfaction is studied and proved,thus enriching the theory of fuzzy measure.

关 键 词：F连续非可加测度 λ模糊算子 模糊拟积概率积分 

分 类 号：O29[理学—应用数学]