一种信度马尔科夫模型及应用

A Belief Markov Model and Its Application

马尔科夫链以其无后效性广泛应用于自然科学和工程技术领域.经典的马尔科夫链并不能反映对象状态的不确定性,并且当状态划分边界过于清晰时,状态转移情况不稳定.为了保持状态转移的稳定性以及能够有效地表示和处理对象状态的不确定性,本文提出了一种信度马尔科夫模型.新模型引入了Dempster-Shafer(DS)证据理论来描述对象状态的不确定性,将对象的所有状态归类为一个辨识框架,建立基本概率指派函数,然后生成一个命题转移概率矩阵,最后根据对象当前的状态得到将来的状态.本文提出的信度马尔科夫模型是对经典马尔科夫链的推广,向下兼容了它的性质.实例表明,新模型克服了上述缺陷,获得了较经典马尔科夫链更加合理、准确的结果,具有更高的有效性和实用性.

Markov chain is widely applied to the fields of natural science and engineering technology with its non-aftereffect property.However,the classical Markov chain is unable to handle the uncertainty of state description.Besides,the state s transition is unstable when the divide boundary of states is too clear.In order to overcome these limitations,a belief Markov model is proposed in this paper.Dempster-Shafer（DS） theory of evidence is introduced to new model to represent the uncertainty of states.Firstly,the states are reduced to form a frame of discernment,and a basic probability assignment function is established.Then,as an intermediate result,a matrix of propositional transition probability is calculated.Finally,the future state can be obtained according to the current state.The proposed belief Markov model is a generalization of classical Markov chain and downward compatible with its properties.A case study shows that the limitations above mentioned are overcame and the proposed model is more effective and practicable.