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.
作者
孙荣
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)
出处
《模糊系统与数学》
北大核心
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)。
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
Topological Approach
Fuzzy Pseudometric
Generalized Regularity
Completion
The Symmetric Fuzzy Measure Space
