By Irina Georgescu

ISBN-10: 3540689974

ISBN-13: 9783540689973

ISBN-10: 3540689982

ISBN-13: 9783540689980

The foundations of published choice conception for a aggressive patron have been laid through Samuelson in 1938. Later this idea used to be axiomatically constructed by means of Arrow, Sen, Suzumura and different economists into the speculation of selection functions.

This booklet extends the speculation of published choice to fuzzy selection features and offers purposes to multicriteria selection making difficulties. the most subject matters of published choice conception (rationality, published choice and congruence axioms, consistency stipulations) are handled within the framework of fuzzy selection services. New subject matters, comparable to the measure of dominance and similarity of obscure offerings, are constructed. the consequences acquired are utilized to fiscal difficulties the place partial details and human subjectivity contain imprecise offerings and obscure personal tastes. The ebook incorporates a variety of new effects accomplished via the writer. although the textual content is fairly self-contained, past wisdom of printed choice and fuzzy set thought is beneficial for the reader.

Social selection theorists and desktop scientists will locate during this monograph stimulating fabric for extra examine and urban applications.

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Extra resources for Fuzzy Choice Functions: A Revealed Preference Approach

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E. C(S) = {x}. By identifying the set {x} with its element x, we can consider that X is the range of f , that means f : B → X. By definition, a choice problem has the form ((X, B), C) where (X, B) is a choice space and C is a choice function on (X, B). Considering the available sets as criteria in decision–making, a choice problem can be viewed as a decision–making problem. A significant part of choice function theory [8], [91], [92], [93] has been developed under the following hypothesis: (H) B contains all non-empty finite subsets of X.

If Q has a property P and Q is the G–rationalization (resp. the M – rationalization) of C then we shall say that C is P –G–rational ( resp. P –M – rational ). For example, if Q is a transitive preference relation then C is said to be transitive G–rational (resp. transitive M –rational). 12. ([100], p. 158) Let X = {a, b, c} and B = {S1 , S2 } where S1 = {x, y}, S2 = {y, z}. Let us consider the choice function C on (X, B) defined by C(S1 ) = {x}, C(S2 ) = {y, z} and the following binary relations on X: Q1 = Q1 = {(x, y), (y, z), (z, y)}; Q2 = {(x, y), (y, z), (z, y), (x, z), (z, x)}; Q2 = {(x, y)}.

96] Let (X, P(X) \ { ∅}) be a finite choice space. If Q is a reflexive, transitive and total (=regular) preference relation on X then GQ and MQ are choice functions on (X, B). 16. [96] Let (X, P(X) \ { ∅}) be a finite choice space and Q a reflexive and complete preference relation on X. Then the following are equivalent: (1) GQ is a choice function; (2) Q is acyclic. Under these circumstances MQ is a choice function too. So far we have presented two ways in which two choice functions correspond to a preference relation Q on X : Q −→ GQ and Q −→ MQ .

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Fuzzy Choice Functions: A Revealed Preference Approach by Irina Georgescu

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