A Markov-type hybrid process with discrete parameters is constructed from credibilistic kernels and stochastic kernels. To evaluate a hybrid reward process, a discounted total expected value is defined, which is characterized as a fixed point of the corresponding operator. Also, examples are given.
a b s t r a c tUsing a concept of random fuzzy variables in credibility theory, we formulate a credibilistic model for unichain Markov decision processes under average criteria. And a credibilistically optimal policy is defined and obtained by solving the corresponding nonlinear mathematical programming. Also we give a computational example to illustrate the effectiveness of our new model.
This paper is concerned with the optimality gap between perfectly precise information and fuzzy one for uncertain Markov Decision Processes (MDPs). Introducing a fuzzification operator L σ with the deviation parameter σ(0 ≤ σ < ∞) , the fuzzy information for the unknown transition matrices is described as the L σ -value of the true transition matrices. The range of σ which does not make the optimality gap between the true-valued MDPs and the MDPs induced by L σ is characterized and obtained by the corresponding inequalities. These theoretical results are applied to a numerical example of a machine maintenance problem.
We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.
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