Authors:
Karla Carrero-Vera
1
;
Hugo Cruz-Suárez
1
and
Raúl Montes-de-Oca
2
Affiliations:
1
Benemérita Universidad Autónoma de Puebla, Av. San Claudio y Río Verde, Col. San Manuel, CU, Puebla, Pue. 72570, Mexico
;
2
Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Ciudad de México 09340, Mexico
Keyword(s):
Markov Decision Processes, Dynamic Programming, Optimal Policy, Fuzzy Sets, Triangular Fuzzy Numbers.
Abstract:
This paper concerns discounted Markov decision processes with a fuzzy reward function triangular in shape.
Starting with a usual and non-fuzzy Markov control model (Hernández-Lerma, 1989) with compact action ´
sets and reward R, a control model is induced only substituting R in the usual model for a suitable triangular
fuzzy function R˜ which models, in a fuzzy sense, the fact that the reward R is “approximately” received. This
way, for this induced model a discounted optimal control problem is considered, taking into account both a
finite and an infinite horizons, and fuzzy objective functions. In order to obtain the optimal solution, the partial
order on the α-cuts of fuzzy numbers is used, and the optimal solution for fuzzy Markov decision processes
is found from the optimal solution of the corresponding usual Markov decision processes. In the end of the
paper, several examples are given to illustrate the theory developed: a model of inventory system, and two
others more
in an economic and financial context.
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