模糊马尔可夫链状态取值及其机会测度函数  

State Value of Fuzzy Markov Chain and Its Chance Measure Function

作　　者：刘兆君[1] Liu Zhaojun(School of Mathematics and Information Science,Shandong Technology and Business University,Yantai Shandong 264005,China)

机构地区：[1]山东工商学院数学与信息科学学院,山东烟台264005

出　　处：《统计与决策》2021年第14期29-32,共4页Statistics & Decision

摘　　要：文章依据模糊随机变量的定义和模糊条件概率的定义,给出模糊状态的马尔可夫链的数学定义,分析模糊状态转移概率的计算方法,结合已有的模糊加权马尔可夫链的研究方法,计算得到预测对象出现各模糊状态的模糊概率。根据模糊随机理论,考虑模糊随机变量均值与机会测度,刻画预测对象的可能状态取值变化规律,并得到其可能状态取值的机会测度预测函数曲线,对模糊马尔可夫链的状态变化实现深度预测,拓展了模糊马尔可夫链的适用范围。According to the definition of fuzzy random variable and that of fuzzy conditional probability,this paper gives the mathematical definition of Markov chain in fuzzy state,analyzes calculation method of fuzzy state transition probability,and combines with the existing research method of fuzzy weighted Markov chain to calculate the fuzzy probability of each fuzzy state of the predicted object.And then,based on fuzzy random theory,the paper considers the fuzzy random variable mean value and chance measure to describe the variation rule of the possible state value of the predicted object,and obtains the chance measure prediction function curve of the possible state values.Finally,the paper realizes the depth prediction of state change of fuzzy Markov chain,and expands the application range of fuzzy Markov chain.

关 键 词：马尔可夫链 模糊转移概率矩阵 模糊随机变量 模糊随机均值 机会测度 

分 类 号：O211.6[理学—概率论与数理统计]