Master of Science in Electrical Engineering (MSEE)
Electrical and Computer Engineering
Markov decision processes have become an indispensable tool in applications as diverse as equipment maintenance, manufacturing systems, inventory control, queuing networks and investment analysis. Typically we have a controlled Markov chain on a suitable state space in which transitional probabilities depend on the policy (or decision maker) which comes from a set of possible actions. The main problem of interest would be to find an optimal policy that minimizes the associated cost. Linear Programming has been widely used to find the optimal Markov decision policy. It requires solutions of large systems of simultaneous linear equations. By the fact that the complexity in linear programming increases much faster with the increase in the number of states which is often called curse of dimensionality, the linear programming method can handle only small models. This thesis presents a new method to lessen the curse of dimensionality. By assuming certain monotonicity property for the transition probability, it is shown that a fuzzy membership function can be used to reduce the number of states. The use of membership functions help to reduce the number of the states. However all the states remain intact through the use of the membership value. That is, those states eliminated can be recovered through interpolation with the aid of membership functions. This new proposed method is shown to be effective in coping with the curse of dimensionality.
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Irshad, Ahmed Syed, "Fuzzifying [sic] Markov decision process" (2005). LSU Master's Theses. 1373.