Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Mathematics

Esteban Induráin¹  Armajac Raventós-Pujol²  MaríaJ. Campión² 

[1] Institute for Advanced Materials and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain;Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain;

关键词: arrow’s impossibility theorems;    mathematical social choice;    fuzzy preferences;    decomposition of preferences;    aggregation of individual profiles;    social rules;    arrovian models;    paretian property;    independence of irrelevant alternatives;    dictatorship;   

DOI  :  10.3390/math8030436

来源: DOAJ

【 摘 要 】

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

【 授权许可】

Unknown