On optimality gaps for fuzzification in finite Markov decision processes

Abstract

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.

Credibilistic Markov decision processes: The average case

“…Also, by the same idea as above Kageyama [7] has treated the fuzzy information by a fuzzification operator with a deviation parameter and considered the model-identification problem for various values of the deviation parameter.…”