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Discounted Markov decision processes with fuzzy costs

Author

Listed:
  • Abdellatif Semmouri

    (Sultan Moulay Slimane University)

  • Mostafa Jourhmane

    (Sultan Moulay Slimane University)

  • Zineb Belhallaj

    (Sultan Moulay Slimane University)

Abstract

Fuzzy theory is a discipline that has recently appeared in the mathematical literature. It generalizes classic situations. Therefore, its success continues to increase and to keep going up from time to time. In this work, we consider the model of Markov decision processes where the information on the costs includes imprecision. The fuzzy cost is represented by the fuzzy number set and the infinite horizon discounted cost is minimized from any stationary policy. This paper presents in the first part the notion of fuzzy sets and some axiomatic basis and relevant concepts with fuzzy theory in short. In second part, we propose a new definition of total discounted fuzzy cost in infinite planning horizon. We will compute an optimal stationary policy that minimizes the total fuzzy discounted cost by a new approach based on some standard algorithms of the dynamic programming using the ranking function concept. The last adapted criterion has many applications in several areas such that the forest management, the management of energy consumption, the finance, the communication system (mobile networks).

Suggested Citation

  • Abdellatif Semmouri & Mostafa Jourhmane & Zineb Belhallaj, 2020. "Discounted Markov decision processes with fuzzy costs," Annals of Operations Research, Springer, vol. 295(2), pages 769-786, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:2:d:10.1007_s10479-020-03783-6
    DOI: 10.1007/s10479-020-03783-6
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Pelin Canbolat & Uriel Rothblum, 2013. "(Approximate) iterated successive approximations algorithm for sequential decision processes," Annals of Operations Research, Springer, vol. 208(1), pages 309-320, September.
    3. Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2020. "Markov perfect equilibria in a dynamic decision model with quasi-hyperbolic discounting," Annals of Operations Research, Springer, vol. 287(2), pages 573-591, April.
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