FROM FUZZY SET-THEORY TO NONADDITIVE PROBABILITIES - HOW HAVE ECONOMISTS REACTED
In this paper, we are going to try to conduct a comparative review of the two programmes (devoted to the application of fuzzy sets theory in economics for the first and to nonadditive probabilities for the second) while putting forward some explanations and conjecture as to their development and their future. In Section 1, we defend the thesis which claims that the first programme has only had a global focus on the approach in terms of generalization and we shall go deeper into the analysis of the particular area of General Equilibrium as it is the programme on which Ponsard worked the most. In Section 2, we shall seek to show that the second programme, devoted to the introduction of nonadditive probabilities in decision theory, on the contrary, has attempted to come up with independent findings. This would explain why this last programme has managed to fit into topics at a standstill or in crisis easily (which is undeniably the case of the standard theory of decision making) while the first programme was only envisaged as a kind of mathematical game involving the application of new rules to an old model. In the case of the first programme, one might thus speak of an extension principle and in the second case of a resolution principle.
nonadditive probabilities microeconomics fuzzy preference