基于模糊伪度量的Riesz空间值模糊测度空间的完备化  

Completion of Riesz Space-valued Fuzzy Measures Space Using Fuzzy Pseudometrics

作　　者：孙荣[1,2] SUN Rong(Dept of Math and Statistics,,Chongqing University of Technol and Business,Chongqing 400067,China;Chongqing Key Laboratory of Social Economic and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]社会经济应用统计重庆市重点实验室,重庆400067

出　　处：《模糊系统与数学》2020年第4期16-23,共8页Fuzzy Systems and Mathematics

基　　金：国家社会科学基金资助项目(19BTJ020)。

摘　　要：本文研究了模糊测度在模糊集上的延拓问题,得出了在广义正则条件下取值于Riesz空间子集的每一个模糊测度都可以唯一地从广义模糊σ-环延拓到由其生成的模糊σ-域的结论。利用我们所提出的模糊伪度量,得到了实现Riesz空间值对称模糊测度空间完备化的拓扑方法。This study considers the extension of fuzzy measures on a class of fuzzy sets. Every fuzzy measure on a class of fuzzy sets with values in a subset of a Riesz space can be uniquely extended from a generalized fuzzy σ-ring to the fuzzy σ-algebra generated by it under the generalized regularity condition. The main result is that a topological approach to completion of Riesz space-valued symmetric fuzzy measure space using the fuzzy pseudometrics proposed in the paper is found.

关 键 词：拓扑方法 模糊伪度量 广义正则 完备化 对称模糊测度空间 

分 类 号：O159[理学—数学]