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In this paper, we consider the model that the information on the rewards in vector-valued Markov decision processes includes imprecision or ambiguity. The fuzzy reward model is analyzed as follows: The fuzzy reward is represented by the fuzzy set on the multi-dimensional Euclidian space R p and the infinite horizon fuzzy expected discounted reward(FEDR)… (More)

We consider utility-constrained Markov decision processes. The expected utility of the total discounted reward is maximized subject to multiple expected utility constraints. By introducing a corresponding Lagrange function, a saddle-point theorem of the utility constrained optimization is derived. The existence of a constrained optimal policy is… (More)

In this note, we give four versions of Egoroff's theorem in non-additive measure theory by using condition (E), the pseudo-condition (E) of set function and the duality relations between the conditions. These conditions offered are not only sufficient but also necessary for the four kinds of Egoroff's theorems.

This paper discusses two topics on fuzzy random variables in decision making. One is a new evaluation method of fuzzy random variables, and the other is to present a mathematical model in financial engineering by fuzzy random variables. The evaluation method is introduced as mean values defined by fuzzy measures, and it is also applicable to fuzzy numbers… (More)

We formulate a stopping problem for dynamic fuzzy systems concerning with fuzzy decision environment. It could be regarded as a natural fuzzification of non-fuzzy stopping problem with a deterministic dynamic system. The validity of the approach by α-cuts of fuzzy sets will be discussed in constructing One-step Look Ahead policy of an optimal fuzzy stopping… (More)

The paper deals with a p person, non-cooperative game related to the observation of a Markov chain. The players observe the process up to a random moment deened by a monotonic logical function based on an individual players' decision. The concept of Nash equilibrium is used. The solution of the game for nite and innnite horizon problems is derived. A simple… (More)

- Masami Kurano, Masami Yasuda, Junichi Nakagami
- 2009

This paper studies the stopping problem for random vectors of p components which correspond to the payoffs to a group of p players. The observation proCt~SS is stopped at the first time when no less than r(1 ";;;'r";;;'p) players declare to stop. We call it a majority rule. TIle object of this paper is to find out a reasonable stopping strategy under a… (More)

- M. Kurano, Masami Yasuda, J. Nakagami
- 1999

In this paper, the average cases of Markov decision processes with uncertainty is considered. That is, a controlled Markov set-chain model with a finite state and action space is developed by an interval arithmetic analysis, and we will find a Pareto optimal policy which maximizes the average expected rewards over all stationary policies under a new partial… (More)

In this paper, we show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusin's theorem, which is well-known in classical measure theory, is generalized to fuzzy measure space by using the regularity and weakly null-additivity. A version of Egoroo's theorem for the fuzzy measure deÿned on metric spaces is given. An application… (More)

In this paper, we formulate the fuzzy perceptive model for discounted Markov decision processes in which the perception for transition probabilities is described by fuzzy sets. The optimal expected reward, called a fuzzy perceptive value, is characterized and calculated by a new fuzzy relation. As a numerical example, a machine maintenance problem is… (More)