Application of Fuzzy Logic to Social Choice Theory

Book description

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.

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.

Table of contents

  1. Cover
  2. Contents
  3. Preface
  4. Chapter 1: Fuzzy Maximal Subsets (1/4)
  5. Chapter 1: Fuzzy Maximal Subsets (2/4)
  6. Chapter 1: Fuzzy Maximal Subsets (3/4)
  7. Chapter 1: Fuzzy Maximal Subsets (4/4)
  8. Chapter 2: Fuzzy Choice Functions (1/10)
  9. Chapter 2: Fuzzy Choice Functions (2/10)
  10. Chapter 2: Fuzzy Choice Functions (3/10)
  11. Chapter 2: Fuzzy Choice Functions (4/10)
  12. Chapter 2: Fuzzy Choice Functions (5/10)
  13. Chapter 2: Fuzzy Choice Functions (6/10)
  14. Chapter 2: Fuzzy Choice Functions (7/10)
  15. Chapter 2: Fuzzy Choice Functions (8/10)
  16. Chapter 2: Fuzzy Choice Functions (9/10)
  17. Chapter 2: Fuzzy Choice Functions (10/10)
  18. Chapter 3: Factorization of Fuzzy Preference Relations (1/9)
  19. Chapter 3: Factorization of Fuzzy Preference Relations (2/9)
  20. Chapter 3: Factorization of Fuzzy Preference Relations (3/9)
  21. Chapter 3: Factorization of Fuzzy Preference Relations (4/9)
  22. Chapter 3: Factorization of Fuzzy Preference Relations (5/9)
  23. Chapter 3: Factorization of Fuzzy Preference Relations (6/9)
  24. Chapter 3: Factorization of Fuzzy Preference Relations (7/9)
  25. Chapter 3: Factorization of Fuzzy Preference Relations (8/9)
  26. Chapter 3: Factorization of Fuzzy Preference Relations (9/9)
  27. Chapter 4: Fuzzy Non-Arrow Results (1/5)
  28. Chapter 4: Fuzzy Non-Arrow Results (2/5)
  29. Chapter 4: Fuzzy Non-Arrow Results (3/5)
  30. Chapter 4: Fuzzy Non-Arrow Results (4/5)
  31. Chapter 4: Fuzzy Non-Arrow Results (5/5)
  32. Chapter 5: Fuzzy Arrow's Theorem (1/8)
  33. Chapter 5: Fuzzy Arrow's Theorem (2/8)
  34. Chapter 5: Fuzzy Arrow's Theorem (3/8)
  35. Chapter 5: Fuzzy Arrow's Theorem (4/8)
  36. Chapter 5: Fuzzy Arrow's Theorem (5/8)
  37. Chapter 5: Fuzzy Arrow's Theorem (6/8)
  38. Chapter 5: Fuzzy Arrow's Theorem (7/8)
  39. Chapter 5: Fuzzy Arrow's Theorem (8/8)
  40. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (1/7)
  41. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (2/7)
  42. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (3/7)
  43. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (4/7)
  44. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (5/7)
  45. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (6/7)
  46. Chapter 6: Single Peaked Fuzzy Preferences: Black's Median Voter Theorem (7/7)
  47. Chapter 7: Rationality (1/6)
  48. Chapter 7: Rationality (2/6)
  49. Chapter 7: Rationality (3/6)
  50. Chapter 7: Rationality (4/6)
  51. Chapter 7: Rationality (5/6)
  52. Chapter 7: Rationality (6/6)
  53. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (1/10)
  54. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (2/10)
  55. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (3/10)
  56. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (4/10)
  57. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (5/10)
  58. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (6/10)
  59. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (7/10)
  60. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (8/10)
  61. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (9/10)
  62. Chapter 8: Arrow-Type Results under Intuitionistic Fuzzy Preferences (10/10)
  63. Chapter 9: Manipulability of Fuzzy Social Choice Functions (1/4)
  64. Chapter 9: Manipulability of Fuzzy Social Choice Functions (2/4)
  65. Chapter 9: Manipulability of Fuzzy Social Choice Functions (3/4)
  66. Chapter 9: Manipulability of Fuzzy Social Choice Functions (4/4)
  67. Chapter 10: Similarity of Fuzzy Choice Functions (1/6)
  68. Chapter 10: Similarity of Fuzzy Choice Functions (2/6)
  69. Chapter 10: Similarity of Fuzzy Choice Functions (3/6)
  70. Chapter 10: Similarity of Fuzzy Choice Functions (4/6)
  71. Chapter 10: Similarity of Fuzzy Choice Functions (5/6)
  72. Chapter 10: Similarity of Fuzzy Choice Functions (6/6)
  73. Back Cover

Product information

  • Title: Application of Fuzzy Logic to Social Choice Theory
  • Author(s): John N. Mordeson, Davender S. Malik, Terry D. Clark
  • Release date: March 2015
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781482250992