Fuzzy set-valued stochastic Lebesgue integral
- 作者：Jungang Li lijg@bjtu.edu.cn ; Jinting Wang ; jtwang@bjtu.edu.cn
- 关键词：Fuzzy number ; Fuzzy set-valued stochastic process ; Fuzzy random variable ; Fuzzy stochastic Lebesgue integral ; Level set process
- 刊名：Fuzzy Sets and Systems
- 出版年：2012
- 期刊代码：55_01650114
- 类别：cp
- 出版时间：1 August, 2012
- 卷：200
- 期：Complete
- 页码：48-64
- 文件大小：267 K
摘要
This paper studies Lebesgue integral of a fuzzy closed set-valued stochastic process with respect to the time t. Firstly, a progressively measurable fuzzy closed set-valued stochastic process is discussed and an almost everywhere problem in the former Aumann type Lebesgue integral of the level-set process is pointed out. Secondly, a new definition of the Lebesgue integral by decomposable closure is given, focusing on Aumann representation theorem, representation theorem and property of convexity. It is proved that the fuzzy closed set-valued stochastic Lebesgue integral is a fuzzy closed set-valued stochastic process which is widely used in the fuzzy world with randomness. Finally, the fuzzy closed set-valued stochastic Lebesgue integral in -space is studied, especially on an almost everywhere problem.