Arrow theorems in the fuzzy setting

Document Type : Research Paper


1 Inarbe (Institute for Advanced Research in Business and Economics) and Departamento de Estadstica, Informaticay Matematicas. Universidad Publica de Navarra. 31006 Pamplona, Spain.

2 InaMat (Institute for Advanced Materials) and Departamento de Estadstica, Informatica y Matematicas. Universidad Publica de Navarra. 31006 Pamplona, Spain.


Throughout this paper, our  main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical  model. But others lead to possibility results. We explore the main grounds that lead to impossibility or possibility. In this analysis,   representative examples arise. One of them corresponds to an impossibility result, and the other ones allow the aggregation  of fuzzy individual preferences to an individual one. We introduce new techniques for the proofs, specially for the one that leads to impossibility.