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
Summary
This is one of the first books to apply fuzzy logic to social choice theory. The book first discusses the rationalization of choice functions and the factorization of fuzzy preference relations. It then covers various solution sets used with the problem of cycling. It also explores Arrow's famous impossibility theorem, Black's median voter theorem, and the Gibbard-Satterthwaite theorem. The book concludes with the implications of intuitionistic fuzzy set logic for Arrow's impossibility theorem
