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Master's Dissertation
DOI
10.11606/D.45.2017.tde-03102017-172807
Document
Author
Full name
Rafael Hernandez Jabur
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Tonelli, Pedro Aladar (President)
Barros, Laécio Carvalho de
Silva, Marcos Fernandes Gonçalves da
Title in Portuguese
Teorema de Arrow-Sen e teoria da escolha fuzzy
Keywords in Portuguese
Arrow-Sen
Função de escolha
Fuzzy
Racionalidade
Abstract in Portuguese
Racionalidade é um importante tema para a economia e qualquer outra área que se dedica à tomada de decisão. Ao longo do século XX, economistas deram diferentes definições do que seria um comportamento racional. Tais definições foram formalizadas matematicamente e, mediante uma hipótese plausível, mostradas equivalentes no teorema de Arrow- Sen. Após o surgimento da teoria de conjuntos fuzzy, diferentes autores se debruçaram na expansão através da matemática fuzzy de tais definições e equivalências. Este trabalho retoma o histórico dessas definições e a passagem da formalização clássica para a fuzzy. Também expõe resultados obtidos com provas alternativas e exemplos que mostram as limitações das equivalências numa abordagem sob a ótica da teoria de conjuntos fuzzy.
Title in English
Arrow-Sen theorem and fuzzy choice theory
Keywords in English
Arrow-Sen
Choice function
Fuzzy
Rationality
Abstract in English
Rationality is among the most important subjects in economics and the study of decisionmaking process. Different definitions of what is a rational behavior were given in the 20th century. The Arrow-Sen theorem shows that such definitions are equivalent under a plausible hypothesis. With the development of fuzzy theory, a fuzzy approach to this problem was given by different authors. This work shows this historical development of the definitions and the transition from the classical to the fuzzy view. It also presents the results obtained with alternative proofs and examples that show the limitations of the equivalences in the fuzzy setup.
 
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Publishing Date
2017-10-06
 
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