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Application of fuzzy logic to social choice theory / John N. Mordeson, Davender S. Malik and Terry D. Clark.

By: Contributor(s): Material type: TextTextSeries: Monographs and research notes in mathematicsPublication details: Boca Raton : CRC Press, c2015.Description: xi, 340 p. ; 24 cmISBN:
  • 9781482250985 (alk. paper)
Subject(s): DDC classification:
  • 302.1301511313 23 M834
Contents:
1. Fuzzy maximal subsets -- 2. Fuzzy choice functions -- 3. Factorization of fuzzy preference relations -- 4. Fuzzy non-arrow results -- 5. Fuzzy Arrow's theorem -- 6. Single peaked fuzzy preferences : Black's median voter theorem -- 7. Rationality -- 8. Arrow-type results under intuitionistic fuzzy preferences -- 9. Manipulability of fuzzy social choice functions -- 10. Similarity of fuzzy choice functions -- Index.
Summary: The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow’s theorem, and Black’s median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard–Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu’s degree of similarity of two fuzzy choice functions.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 302.1301511313 M834 (Browse shelf(Opens below)) Available 136546
Total holds: 0

Includes bibliographical references and index.

1. Fuzzy maximal subsets --
2. Fuzzy choice functions --
3. Factorization of fuzzy preference relations --
4. Fuzzy non-arrow results --
5. Fuzzy Arrow's theorem --
6. Single peaked fuzzy preferences : Black's median voter theorem --
7. Rationality --
8. Arrow-type results under intuitionistic fuzzy preferences --
9. Manipulability of fuzzy social choice functions --
10. Similarity of fuzzy choice functions --
Index.

The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow’s theorem, and Black’s median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard–Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu’s degree of similarity of two fuzzy choice functions.

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