Springer Fuzzy Choice Functions: A Revealed Preference Approach: 214 (Studies in Fuzziness and Soft Computing, 214)

This book extends the theory of revealed preference to fuzzy choice functions, providing applications to multicriteria decision making problems. The main topics of revealed preference theory are treated in the framework of fuzzy choice functions. New topics, such as the degree of dominance and similarity of vague choices, are developed. The results are applied to economic problems where partial information and human subjectivity involve vague choices and vague preferences. Review From the reviews: "This book, based on the author’s PhD thesis, is an excellent extension of the revealed preference theory to the fuzzy case where preference and choice are fuzzy. … is basically a mathematic text, it is highly recommended to choice theorists and to specialists in fuzzy mathematics. Choice theorists will discover the interest of using fuzziness to deal with a more realist universe and mathematicians working on fuzziness will see how fuzzy mathematics can be used in a highly theoretical part of social science." (Maurice Salles, Zentralblatt MATH, Vol. 1130 (8), 2008) From the Back Cover The foundations of revealed preference theory for a competitive consumer were laid by Samuelson in 1938. Later this theory was axiomatically developed by Arrow, Sen, Suzumura and other economists into the theory of choice functions. This book extends the theory of revealed preference to fuzzy choice functions and provides applications to multicriteria decision making problems. The main topics of revealed preference theory (rationality, revealed preference and congruence axioms, consistency conditions) are treated in the framework of fuzzy choice functions. New topics, such as the degree of dominance and similarity of vague choices, are developed. The results obtained are applied to economic problems where partial information and human subjectivity involve vague choices and vague preferences. The book contains a number of new results achieved by the author. Even though the text is reasonably self-contained, previous knowledge of revealed preference and fuzzy set theory is helpful for the reader. Social choice theorists and computer scientists will find in this monograph stimulating material for further research and concrete applications.