Perceptive Evaluation for the Optimal Discounted Reward in Markov Decision Processes

Abstract

Abstract. We formulate a fuzzy perceptive model for Markov decision processes with discounted payoff in which the perception for transition probabilities is described by fuzzy sets. Our aim is to evaluate the optimal expected reward, which is called a fuzzy perceptive value, based on the perceptive analysis. It is characterized and calculated by a certain fuzzy relation. A machine maintenance problem is discussed as a numerical example.

A Fuzzy Perceptive Value for Multi-Variate Stopping Problem With a Monotone Rule

“…The perceptive analysis developed in this paper is related to our previous works. A model of stopping problems is formulated in Kurano et al (2004) and that of Markov decision processes is in Kurano et al (2005a) and Kurano et al (2005b). However the basic assumption implemented in the previous stopping problem is different from this paper.…”

An extended version of average Markov decision processes on discrete spaces under fuzzy environment

“…In [3], a fuzzy total expected reward criterion is analyzed for an MDP with finite state space and with a trapezoidal fuzzy reward function. On the other hand, one of the most studied criteria in the literature is the discounted total expected reward/cost, see, for instance, [2,14,15,16,17] and [25]. In these works, the fuzzy approach is applied either in the reward/cost function ( [2,14,15,25]) or in the dynamic of the system ( [14,16,17]), all of them under finite state and action spaces framework.…”

“…On the other hand, one of the most studied criteria in the literature is the discounted total expected reward/cost, see, for instance, [2,14,15,16,17] and [25]. In these works, the fuzzy approach is applied either in the reward/cost function ( [2,14,15,25]) or in the dynamic of the system ( [14,16,17]), all of them under finite state and action spaces framework. In regards to the long-run expected average cost criterion, only the following two works were found: [10] and [13].…”