La décision et les ensembles flous : contributions méthodologiques à la théorie des jeux et l'aide à la décision

Abstract : Determining the allocation and the distribution of scarce resources is fundamental in economics. Thus, decision theory is the cornerstone of economic theory. In this thesis, we first provide a state of the art insisting on the fact that information, that is a central element of decision-making, is imperfect. Secondly, using fuzzy set theory, which aims to capture imprecision, we construct a fuzzy number, so-called C-Shape that captures the sensitivity of the decision-maker. Thirdly, we study decision theory through two key concepts of operation research: (1) game theory and (2) multi-criteria decision making. We provide an analogy between the gauge functions of convex sets and the membership functions arising in fuzzy set theory. Coupling a suitable notion of -convexity with the C-Shape function, we introduce a class of games for which the players can be optimistic, pessimistic or neutral. In addition the existence of Nash equilibrium is proved for such a class of games. Finally, concerning multi-criteria decision analysis, we use the C-Shape functions to characterize a new type of criteria called C-Shape pseudo-criterion, which makes possible to consider the alternatives as substitutable. This should be of interest to take into account, for example, the institutional context in which decision-making is taken.
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Jérémie Mauranyapin. La décision et les ensembles flous : contributions méthodologiques à la théorie des jeux et l'aide à la décision. Economies et finances. Université de Perpignan, 2018. Français. ⟨NNT : 2018PERP0059⟩. ⟨tel-02162299⟩

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