Credibilistic Markov decision processes: The average case

Abstract

a b s t r a c tUsing a concept of random fuzzy variables in credibility theory, we formulate a credibilistic model for unichain Markov decision processes under average criteria. And a credibilistically optimal policy is defined and obtained by solving the corresponding nonlinear mathematical programming. Also we give a computational example to illustrate the effectiveness of our new model.

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

“…for all i ∈ X and a ∈ A(i), then the fuzzy optimal control problem described in (10) and ( 11) is reduced to the optimal control problem described in (5) (See also Remark 2.8. )…”

“…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]. In [13], a Pareto optimal policy maximizing the average expected fuzzy reward under the max-order is found.…”

“…In [13], a Pareto optimal policy maximizing the average expected fuzzy reward under the max-order is found. And, in [10], using the concept of the random fuzzy variable in credibility theory they introduce a new model, called credibilistic MDPs, in order to treat the unknown transition matrices of classical MDPs with credibilistic information; it is important to mention that in both cases the expected average cost is analyzed under the assumption that the state and action spaces are finite.…”

Discrete-time hybrid processes and discounted total expected values

“…It is shown in Kageyama (2009) that for any g ∈ K ( ) T n q (g) → g * (n → ∞) with T n 0 q (g) = g * for some n 0 ≥ 1, so that ∪ ∞ n=1 G n = K ( ). Putting ϕ k (g) = ϕ(g, Po(k)) for g ∈ K ( ) and k ≥ 1, we observe from Theorem 2 that if g ∈ G n , ϕ k (g) = Ch(r ≥ t|g, Po(k))dt + αϕ k+1 (T q (g)).…”

Imprecise set and fuzzy valued probability

“…expert opinions or sparse data sets. Highly imprecise probabilistic system could be formalized using the theory of set or fuzzy valued random variables [1], or using the theory of imprecise probability [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”