Discounted Markov decision processes with fuzzy costs
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Discounted Markov decision processes with fuzzy costs Abdellatif Semmouri1
· Mostafa Jourhmane1 · Zineb Belhallaj1
Accepted: 29 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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
1 Introduction Real-world problems are often complex because of the uncertainty inherent in the parameters that define the problem or the situations in which the problem occurs. In Markov decision problems, both traditional probabilities theory (Balbus et al. 2018; Archibald and Possani 2019; Bhulai et al. 2019) and fuzzy theory (Mohammed 2019; Roy et al. 2019; Bahri and Talbi 2020) are interested in handling problems where some parameters are imprecise. Here, the uncertainty may arise due to partial information about the problem or due to information which is not fully reliable. Since fuzziness and randomness differ in nature, each of them has its own tools. The first approach can be applied only to situations whose characteristics are based on random processes, that is, processes in which the occurrence of events is strictly determined by chance. This framework proposes mathematical tools in the form of probability distributions
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Abdellatif Semmouri [email protected] Laboratory of Information Processing and Decision Support, Faculty of Sciences and Techniques, Sultan Moulay Slimane University, B.P. 523 Beni Mellal, Morocco
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Annals of Operations Research Fig. 1 Fuzzy artificial intelligence
and provides specific processing tools that allow the analysis, understanding and discovery of new knowledge. On the other hand, a large class of problems quite often turns out to be complex in the real world because of whose uncertainty is characterized by a nonrandom process. Hence, the fuzzy approach includes construction of models for problems described by the decision maker in naturel language. This aspect of uncertainty is formulated b
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