Advances in Fuzzy Dynamic Programming

Felix Mora-Camino (1) , Elena Mihaela Capitanul (1) , Fabio Krykhtine (2) , Walid Moudani (3) , Carlos Alberto Nunes Cosenza (2)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 COPPE-UFRJ - Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia
3 LU - Lebanese University [Beirut]

This chapter considers the use of fuzzy dual numbers to model and solve through dynamic programming process mathematical programming problems where uncertainty is present in the parameters of the objective function or of the associated constraints. It is only supposed that the values of the uncertain parameters remain in known real intervals and can be modelled with fuzzy dual numbers. The interest of adopting the fuzzy dual formalism to implement the sequential decision-making process of dynamic programming is discussed and compared with early fuzzy dynamic programming. Here, the comparison between two alternatives is made considering not only the cumulative performance but also the cumulative risk associated with previous steps in the dynamic process, displaying the traceability of the solution under construction as it is effectively the case with the classical deterministic dynamic programming process. The proposed approach is illustrated in the case of a long-term airport investment planning problem.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Felix Mora-Camino, Elena Mihaela Capitanul, Fabio Krykhtine, Walid Moudani, Carlos Alberto Nunes Cosenza. Advances in Fuzzy Dynamic Programming. Optimization Techniques for Problem Solving in Uncertainty, IGI Global, pp.116-139, 2018, Chapter 5, 9781522550914. ⟨10.4018/978-1-5225-5091-4.ch005⟩. ⟨hal-02091806⟩