Economic Theory of Fuzzy Equilibria An Axiomatic Analysis [Paperback]

Fuzzy set theory, which started not much more than 20 years ago as a generalization of classical set theory, has in the meantime evolved into an area which scientifically, as well as from the point of view of applications, is recognized as a very valuable contribution to the existing knowledge. This book provides a remarkable contribution to Fuzzy Economics and presents the state of the art in fuzzy theory of value, namely the aggregated model of microeconomics with fuzzy behaviours. It presents an analysis of classical problems with new tools which lead to interesting results.Fuzzy set theory, which started not much more than 20 years ago as a generalization of classical set theory, has in the meantime evolved into an area which scientifically, as well as from the point of view of applications, is recognized as a very valuable contribution to the existing knowledge. This book provides a remarkable contribution to Fuzzy Economics and presents the state of the art in fuzzy theory of value, namely the aggregated model of microeconomics with fuzzy behaviours. It presents an analysis of classical problems with new tools which lead to interesting results.General Introduction.- 1 Individual Fuzzy Relation of Preference.- 1.1 The Fuzzy Binary Relation of Preference.- 1.1.1 Binary Relation and Fuzzy Binary Relation.- 1.1.2 The Fuzzy Preference and its Properties.- 1.2 The Indifference Paradox.- 1.2.1 Reflexivity and Indifference.- 1.2.2 The Axiomatic Solution.- 1.2.3 Solution.- 1.3 Fuzzy Utility Function on a Countable Set.- 1.3.1 Subrelations of Similitude.- 1.3.2 The Transition Operator.- 1.3.3 Utility and Fuzzy Reflexivity.- 1.3.4 Totally Ordered Fuzzy Topological Space.- 1.3.5 A Fuzzy Utility Function.- 1.4 Fuzzy Utility Function on a Convex Set.- 1.4.1 Assumptions on X.- 1.4.2 The Associated Fuzzy Set Xf.- 1.4.3 Analysis of Assumptions.- 1.4.4 Continuity of Fuzzy Preferences.- 1.4.5 Assumption of Continuity for Fuzzy Preferences.- 1.4.6 Preliminary Results.- 1.4.7 ExtelÓ,