Download e-book for iPad: Economic Theory of Fuzzy Equilibria: An Axiomatic Analysis by Antoine Billot

By Antoine Billot

ISBN-10: 3642799493

ISBN-13: 9783642799495

ISBN-10: 3642799515

ISBN-13: 9783642799518

Fuzzy set idea, which began no longer even more than two decades in the past as a generalization of classical set idea, has meanwhile developed into a space which scientifically, in addition to from the viewpoint of purposes, is famous as a truly precious contribution to the prevailing wisdom. This ebook presents a amazing contribution to Fuzzy Economics and provides the cutting-edge in fuzzy conception of worth, specifically the aggregated version of microeconomics with fuzzy behaviours. It provides an research of classical issues of new instruments which bring about attention-grabbing results.

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It produces the criterion which allows to socially compare the elements of the referential set X. The Unanimity Axiom, A3 It means that if all the agents of society S agree to prefer z to y, then society prefers z to y : V(z, y) E X2j Vi E S'I'I~](Y) ~ I'~](z) ~ I'[z](y) ~ I'~](z). The Independence of Irrelevant Alternatives, A4 To compare an object z with an object y, the collectivity forgets about the other objects belonging to the referential set X. The only thing which founds the social preference is 'who prefers z' and 'who prefers y'.

This one proceeds from the choice. If I prefer object A to object B, then I belong to the group of 'the agents preferring A to B'. But, the more A is preferred to B, the more I belong to this group. 1 Imprecise Behavior and Fuzzy Individual Preferences 37 agent who seems to be implicated: this is called the planner's requirement. This approach depends on the nature of preorders of preference. )-reflexive. A. )-Reflexive Fuzzy Relation of Preference Let X be a referential set of objects. {) and defined from X 2 to M = [0,1].

Its fate will be tragic because it cannot decide which peck is going to feed it. Here, we find the idea, already expressed by the french philosopher Vuillemin 1986, according to which preference theory is not a theory of action because sometimes unable to imply implementable decisions without any exogeneous algorithm as uncertainty (heads or tails). 1 Reflexivity and Indifference The means presented by Schmidt 1984 in order to solve this paradox are based on the introduction of a sensibility of preferences relatively to three possible intrinsic characters : good, bad and neutral.

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Economic Theory of Fuzzy Equilibria: An Axiomatic Analysis by Antoine Billot


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