模糊概率随机变量  

Random Variable With Fuzzy Probability

作　　者：吕恩琳[1] 钟佑明[2] 

机构地区：[1]重庆大学工程力学系 [2]重庆大学机械工程学院,重庆400044

出　　处：《应用数学和力学》2003年第4期434-440,共7页Applied Mathematics and Mechanics

摘　　要：研究了第二类模糊随机变量——具有清晰事件、模糊概率的随机变量的数学描述。在区间概率的基础上,利用模糊分解定理给出了概率模糊数集是可行的条件,进一步给出了具有模糊概率的随机变量及模糊概率随机变量的模糊分布函数和模糊分布列的定义和性质。提出并证明了具有模糊概率运算封闭性的模糊概率分解定理。研究了模糊概率随机变量的模糊数学期望和模糊方差的定义和性质。所有关于模糊概率随机变量的数学描述都具有模糊概率运算的封闭性,这为完善模糊概率的运算方法打下了基础。Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem,the feasible condition about a probability fuzzy number set was given,go a step further the definition and characters of random variable with fuzzy probability (RVFP) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.

关 键 词：随机变量 模糊集 概率 数学期望 方差 

分 类 号：O159[理学—数学]