Discounted Markov decision processes with fuzzy costs

Abdellatif Semmouri (), Mostafa Jourhmane and Zineb Belhallaj
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Abdellatif Semmouri: Sultan Moulay Slimane University
Mostafa Jourhmane: Sultan Moulay Slimane University
Zineb Belhallaj: Sultan Moulay Slimane University

Annals of Operations Research, 2020, vol. 295, issue 2, No 11, 769-786

Abstract: 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).

Keywords: Fuzzy optimization; Discounted MDPs; Ranking function (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-020-03783-6

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