Premium
Arrow's theorem under fuzzy rationality
Author(s) -
De Juan Javier Montero
Publication year - 1987
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830320403
Subject(s) - arrow's impossibility theorem , rationality , irrationality , arrow , preference relation , impossibility , mathematical economics , fuzzy logic , mathematics , preference , property (philosophy) , type 2 fuzzy sets and systems , relation (database) , set (abstract data type) , fuzzy set , social choice theory , fuzzy number , epistemology , computer science , artificial intelligence , philosophy , law , programming language , statistics , database , political science
This paper deals with living systems at the individual and group levels. In particular, fuzzy set theory is applied to study Arrow's paradox in aggregation preference problems: such impossibility theorems are based on using the Aristotelian logic; thus Lukasievicz's censure to sciences founded on that logic is also fully applicable. In this paper we deal with “rationality” as a fuzzy property, by suggesting a definition of “fuzzy opinion” different from the classical fuzzy preference relation. Whenever this definition is applied, Arrow's theorems are deemed as results about the impossibility of complete rationality. Nevertheless, the possibility of proving the existence of rules with non‐complete irrationality is revealed.