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.
A stopping problem for a dynamic fuzzy system with fuzzy rewards is formulated, which is thought of as a natural fuzziication of non-fuzzy stopping problem for a determistic dynamic system. And, the validity of the approach by-cuts of fuzzy sets will be discussed in constructing an optimal fuzzy stopping time. Also, a numerical example is given to… (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, the well-known Egoroff's theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor's theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient… (More)
For a dynamic fuzzy system, the fundamental method is to analyze its recursive relation of the fuzzy states. It is similar that the Bellman equation is the important tool in the dynamic programming. Here we will consider the existence and the uniqueness of solution of a fuzzy relational equation. Two examples, which satisses our conditions, are given to… (More)
We shall discuss further regularity properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an… (More)
To solve a mathematical model for American put option with uncertainty , we utilize two essentials, i.e., a λ−weighting function and a mean value of fuzzy random variables simultaneously. Estimation of randomness and fuzziness as uncertainty should be important when we deal with a reasonable and natural model extended from the original optimization/decision… (More)