Fuzzy Choice Functions - A Revealed Preference Approach

As mentioned in the Introduction, it has the following goals: to develop the main topics of revealed preference theory (rationality, revealed preference, congruence, consistency) for a large class of fuzzy choice functions, to explore new topics (degree of dominance, similarity, indicators of rationality) specific to a fuzzy approach to choice functions and to show the manner in which some problems of multicriterial decision making problems can find natural solutions in fuzzy revealed preference theory. a rich bibliography of 120 titles. As mentioned in Concluding Remarks, the contribution of the book consists in the following: (1) it is a theoretical framework for a fuzzy revealed preference theory different of that of Banerjee's; the author develops the fuzzy version of the direction Uzawa-Arrow-Sen. (2) The treatment, in this general framework, of the main topics of revealed preference theory such as rationality, revealed preference and congruence axioms, consistency conditions; the statement of various conditions and results, as well their proofs, is not a simple translation of the situations from the case of crisp choice functions; sometimes, a crisp property has many different fuzzy versions. (3) The definition of the degree of dominance of an alternative as a tool in obtaining the hierarchy of alternatives according to different