Decomposition and arrow-like aggregation of fuzzy preferences
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...
| Authors: | , , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad Pública de Navarra |
| Repository: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/37331 |
| Online Access: | https://hdl.handle.net/2454/37331 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
|---|