模糊随机更新过程的相关理论

【作者】 钟竞英；

【导师】 钱能生；

【作者基本信息】 五邑大学 ， 应用数学， 2008， 硕士

【摘要】 众所周知,1965年Zadeh提出模糊集的概念,1981年Kwakemaak提出了模糊随机变量的定义,1982年Kruse研讨了独立同分布的模糊随机变量序列的强大数定律。基于模糊理论,最近模糊随机更新理论也随之发展起来。模糊随机变量是概率空间到模糊变量集的隶属,基于模糊随机理论,本文介绍了在概率空间(Ω,Г,P)下讨论的独立同分布的时间间隔序列的模糊随机更新过程。给出了模糊随机更新过程的定义、更新过程所满足的更新方程,时间间隔序列的分布函数和模糊随机更新变量之间的关系;模糊更新方程的建立,同时也给出模糊更新方程的性质:随机基本更新定理、模糊随机Blackwell’s更新定理、模糊随机关键更新理论、模糊随机交错更新定理、模糊随机有酬更新定理和模糊随机延迟更新理论、模糊随机Erlang更新理论。更多还原

【Abstract】 In this paper, Fuzzy random variable is a measure function from a probability space(Ω,Γ,P) to a collection of fuzzy variables. Based on the fuzzy random theory, we introduce the concept of fuzzy random renewal processes(FRRP) which were generated by a sequence of independent and identically distributed(idd) fuzzy random interarrival times .address some properties of renewal processes generated by (idd) fuzzy random interarrival times. The relationship between the expected value of the fuzzy random renewal variable and the distributed functions of interarrival times. The fuzzy random renewal equation is provided. Furthermore , fuzzy random elementary renewal theorem, fuzzy random Blackwell’s renewal theorem, fuzzy random key renewal theorem, fuzzy random alternating renewal theorem are given. Finally fuzzy random reward renewal theorem and fuzzy random delayed renewal theorem,fuzzy random Erlang renewal process also established.更多还原