On group decision making, consensus reaching, voting and voting paradoxes under fuzzy preferences and a fuzzy majority: A survey and some perspectives

Studies in Fuzziness and Soft Computing

Volumn 220, Issue , 2008, Pages 263-295

  Kacprzyk, Janusz ^a   Zadrozny, Sławomir ^a   Fedrizzi, Mario ^a   Nurmi, Hannu ^a  

^a NONE

Author keywords

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Indexed keywords

EID: 35648957136     PISSN: 14349922     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-73723-0_14     Document Type: Article

References (87)

1. Aizerman, M.A. (1985). New problems in the general choice theory, Social Choice and Welfare, 2, 235-282.
2. Arrow, K.J. (1963). Social Choice and Individual Values. 2nd Edition. Wiley, New York.
3. Barrett, C.R., Pattanaik, P.K. and Salles, M. (1986). On the structure of fuzzy social welfare functions. Fuzzy Sets and Systems, 19, 1-10.
4. Barrett, C.R., Pattanaik, P.K. and Salles, M. (1990). On choosing rationally when preferences are fuzzy. Fuzzy Sets and Systems, 34, 197-212.
5. Barrett, C.R., Pattanaik, P.K. and Salles, M. (1992). Rationality and aggregation of preferences in an ordinally fuzzy framework. Fuzzy Sets and Systems 49, 9-13.
6. Basu,K, Deb, R. and Pattanaik, P.K. (1992) Soft sets: An ordinal formulation of vagueness with some applications to the theory of choice. Fuzzy Sets and Systems 45, 45-58.
7. Bezdek, J.C., Spillman, B. and Spillman, R. (1978). A fuzzy relation space for group decision theory, Fuzzy Sets and Systems, 1, 255-268.
8. Bezdek, J.C., Spillman, B. and Spillman, R. (1979). Fuzzy relation space for group decision theory: An application, Fuzzy Sets and Systems, 2, 5-14.
9. Blin, J.M. (1974). Fuzzy relations in group decision theory, J. of Cybernetics, 4, 17-22.
10. Blin, J.M. and Whinston, A.P. (1973). Fuzzy sets and social choice, J. of Cybernetics, 4, 17-22.
11. Bordogna, G., Fedrizzi, M. and Pasi, G. (1997) A linguistic modelling of consensus in group decision making based on OWA operators, IEEE Trans. on Systems, Man and Cybernetics, SMC-27, 126-132.
12. Chiclana, F, Herrera, F. and Herrera-Viedma, E. (2001) Integrating multiplicative preference relations in a multipurpose decision making model based on fuzzy preference relations. Fuzzy Sets and Systems, 122, 277-291.
13. Chiclana, F, Herrera, F. and Herrera-Viedma, E. (2001a) Multiperson decision making based on multiplicative preference relations. European Journal of Operational Research, 129, 372-385.
14. Cutello, V. and Montero, J. (1993) A characterization of rational amalgamation operations, International J. of Approximate Reasoning 8, 325-344.
15. Dasgupta, M. and Deb, R. (1996), Transitivity and fuzzy preferences, Social Choice and Welfare, 13, 305-318.
16. DeGrazia, A. (1953), Mathematical Derivation of an Election System, Isis, 44, 42-51.
17. Delgado, M., Verdegay, J.L. and Vila, M.A. (1993). On aggregation operations of linguistic labels, Int. J. of Intelligent Systems, 8, 351-370.
18. Delgado,M., Herrera, F., Herrera-Viedma, E. and Martinez, L. (1998) Combining numerical and linguistic information in group decision making. Information Sciences, 107, 177-194.
19. Fedrizzi, M., Kacprzyk, J. and Nurmi, H. (1993). Consensus degrees under fuzzy majorities and fuzzy preferences using OWA (ordered weighted average) operators, Control and Cybernetics, 22, 71-80.
20. Fedrizzi, M., Kacprzyk, J. and Nurmi, H. (1996). How different are social choice functions: A rough sets approach, Quality and Quantity 30, 87-99.
21. Fedrizzi, M., Kacprzyk, J. and Zadrozny, S. (1988). An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers, Decision Support Systems, 4, 313-327.
22. Fishburn, P.C. (1990). Multiperson decision making: A selective review. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 3-27.
23. Fodor, J. and Roubens, M. (1994) Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht.
24. García-Lapresta, J.L. and Llamazares, B. (2000). Aggregation of fuzzy preferences: Some rules of the mean. Social Choice and Welfare, 17, 673-690.
25. González-Pachón, J., Gómez, D., Montero, J. and Yáñez, J. (2003) Searching for the dimension of valued preference relations, International Journal of Approximate Reasoning, 33, 133-157.
26. Gonzáalez-Pachón, J., Gómez, D., Montero, J. and Yáñez, J. (2003a) Soft dimension theory, Fuzzy Sets and Systems, 137, 137-149.
27. Herrera, F., and Herrera-Viedma, E. (2000) Choice functions and mechanisms for linguistic preference relations. European Journal of Operational Research, 120, 144-161.
28. Herrera, F., Herrera-Viedma, E. and Verdegay, J.L. (1996). A model of consensus in group decision making under linguistic assessments, Fuzzy Sets and Systems, 78, 73-88.
29. Herrera, F., Herrera-Viedma, E. and Verdegay, J.L. (1998) Choice processes for non-homogeneous group decision making in linguistic setting. Fuzzy Sets and Systems, 94, 297-308.
30. Herrera, F., Herrera-Viedma, E. and Verdegay, J.L. (1997) Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making. International Journal of Approximate Reasoning, 16, 309-334.
31. Herrera, F., Herrera-Viedma, E. and Verdegay, J.L. (1997a) A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets and Systems, 88, 31-49.
32. Herrera, F., Martnez, L. (2000) An approach for combining numerical and linguistic information based on the 2-tuple fuzzy linguistic representation model in decision making. International J. of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 539-562.
33. Herrera, F. and Verdegay, J.L. (1995). On group decision making under linguistic preferences and fuzzy linguistic quantifiers. In B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh (Eds.): Fuzzy Logic and Soft Computing, World Scientific, Singapore, pp. 173-180.
34. Intrilligator,M.D. (1973). A probabilistic model of social choice, Review of Economic Studies, 40, 553-560.
35. Intrilligator, M.D. (1982). Probabilistic models of choice, Mathematical Social Sciences, 2, 157-166.
36. Kacprzyk, J. (1984). Collective decision making with a fuzzy majority rule, Proc. of WOGSC Congress, AFCET, Paris, pp. 153-159.
37. Kacprzyk, J. (1985). Zadeh's commonsense knowledge and its use in multicriteria, multistage and multiperson decision making. In M.M. Gupta et al. (Eds.): Approximate Reasoning in Expert Systems, North-Holland, Amsterdam, pp. 105-121.
38. Kacprzyk, J. (1985). Group decision-making with a fuzzy majority via linguistic quantifiers. Part I: A consensory-like pooling; Part II: A competitive-like pooling, Cybernetics and Systems: An International J., 16, 119-129 (Part I), 131-144 (Part II).
39. Kacprzyk, J. (1986). Group decision making with a fuzzy linguistic majority, Fuzzy Sets and Systems, 18, 105-118.
40. Kacprzyk, J. (1987). On some fuzzy cores and "soft" consensus measures in group decision making. In J.C. Bezdek (Ed.): The Analysis of Fuzzy Information, Vol. 2, CRC Press, Boca Raton, pp. 119-130.
41. Kacprzyk, J. (1987). Towards 'human consistent' decision support systems through commonsense-knowledge-based decision making and control models: a fuzzy logic approach, Computers and Artificial Intelligence, 6, 97-122.
42. Kacprzyk, J. and Fedrizzi, M. (1986). "Soft" consensus measures for monitoring real consensus reaching processes under fuzzy preferences, Control and Cybernetics, 15, 309-323.
43. Kacprzyk, J. and Fedrizzi, M. (1988). A "soft" measure of consensus in the setting of partial (fuzzy) preferences, Europ. J. of Operational Research, 34, 315-325.
44. Kacprzyk, J. and Fedrizzi, M. (1989). A 'human-consistent' degree of consensus based on fuzzy logic with linguistic quantifiers, Mathematical Social Sciences, 18, 275-290.
45. Kacprzyk, J. and Fedrizzi, M., Eds. (1990). Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht.
46. Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1992). Group decision making and consensus under fuzzy preferences and fuzzy majority, Fuzzy Sets and Systems, 49, 21-31.
47. Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1997). OWA operators in group decision making and consensus reaching under fuzzy preferences and fuzzy majority. In R.R. Yager and J. Kacprzyk (Eds.): The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer, Boston, pp. 193-206.
48. Kacprzyk, J. and Nurmi, H. (1998) Group decision making under fuzziness, in R. Słowiński (Ed.): Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer, Boston, pp. 103-136.
49. Kacprzyk, J., Nurmi, H. and Fedrizzi, M., Eds. (1996). Consensus under Fuzziness, Kluwer, Boston.
50. Kacprzyk, J., Nurmi H. and Fedrizzi, M. (1999) Group decision making and a measure of consensus under fuzzy preferences and a fuzzy linguistic majority, In L.A. Zadeh and J. Kacprzyk (Eds.): Computing with Words in Information/Intelligent Systems. Part 2. Foundations, Physica-Verlag (Springer-Verlag), Heidelberg and New York, pp. 233-243.
51. Kacprzyk, J. and Roubens, M., Eds. (1988). Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Heidelberg.
52. Kacprzyk, J. and Zadrozny, S. (2002) Collective choice rules in group decision making under fuzzy preferences and fuzzy majority: A unified OWA operator based approach. Control and Cybernetics, 31, 937-948.
53. Kacprzyk, J. and Zadrozny (2003) An Internet-based group decision support system, Management, VII (28), 4-10.
54. Kacprzyk J. and Zadrozny S. (2003) Dealing with imprecise knowledge on preferences and majority in group decision making: Towards a unified characterization of individual and collective choice functions, Bull. of the Polish Academy of Sciences. Tech. Sci., 3, 286-302.
55. Kacprzyk, J., Zadrozny, S. and Fedrizzi, M. (1997). An interactive GDSS for consensus reaching using fuzzy logic with linguistic quantifiers. In D. Dubois, H. Prade and R.R. Yager (Eds.): Fuzzy Information Engineering-A Guided Tour of Applications, Wiley, New York, pp. 567-574.
56. Kelly, J.S. (1978) Arrow Impossibility Theorems. Academic Press, New York.
57. Kelly, J.S. (1978) Social Choice Theory: An Introduction, Academic Press, New York.
58. Kim, J.B. (1983). Fuzzy rational choice functions, Fuzzy Sets and Systems, 10, 37-43.
59. Kuzmin, V.B. and Ovchinnikov, S.V. (1980a). Group decisions I: In arbitrary spaces of fuzzy binary relations, Fuzzy Sets and Systems 4, 53-62.
60. Kuzmin, V.B. and Ovchinnikov, S.V. (1980b). Design of group decisions II: In spaces of partial order fuzzy relations, Fuzzy Sets and Systems, 4, 153-165.
61. Lagerspetz, E. (1995), Paradoxes and representation. Electoral Studies, 15, 83-92.
62. Loewer, B. and Laddaga, R. (1985). Destroying the consensus, in Loewer B., Guest Ed., Special Issue on Consensus, Synthese, 62 (1), pp. 79-96.
63. Montero, J. (1985) A note on Fung-Fu's theorem", Fuzzy Sets and Systems, 13, 259-269.
64. Montero, J. (1987) Arrow's theorem under fuzzy rationality, Behavioral Science, 32, 267-273.
65. Montero, J. (1988) Aggregation of fuzzy opinions in a non-homogeneous group, Fuzzy Sets and Systems, 25, 15-20.
66. Montero, J. (1990) Single-peakedness in weighted aggregation of fuzzy opinions in a fuzzy group, in: Kacprzyk J and Fedrizzi, M. Eds., Multiperson Decision Making Models, Kluwer, Dordrecht, pp. 163-171.
67. Montero, J., Tejada, J. and Cutello, V. (1997) A general model for deriving preference structures from data, European J. of Operational Research, 98, 98-110.
68. Nurmi, H. (1981). Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems, 6, 249-259.
69. Nurmi, H. (1982). Imprecise notions in individual and group decision theory: Resolution of Allais paradox and related problems, Stochastica, VI, 283-303.
70. Nurmi, H. (1983). Voting procedures: A summary analysis, British J. of Political Science, 13, 181-208.
71. Nurmi, H. (1984). Probabilistic voting, Political Methodology, 10, 81-95.
72. Nurmi, H. (1987). Comparing Voting Systems, Reidel, Dordrecht.
73. Nurmi, H. (1997), Referendum design: An exercise in applied social choice theory, Scandinavian Political Studies, 20, 33-52.
74. Nurmi, H. (1998), Voting paradoxes and referenda, Social Choice and Welfare, 15, 333-350.
75. Nurmi, H. (1999), Voting Paradoxes and How to Deal with Them. Springer-Verlag, Berlin-Heidelberg-New York.
76. Nurmi, H. and Kacprzyk, J. (1991). On fuzzy tournaments and their solution concepts in group decision making, Europ. J. of Operational Research, 51, 223-232.
77. Nurmi, H. and Kacprzyk, J. (2000) Social choice under fuzziness: A perspective. In: J. Fodor, B. De Baets and P. Perny (Eds.): Preferences and Decisions under Incomplete Knowledge. PhysicaVerlag (SpringerVerlag), Heidelberg and New York, pp. 107-130.
78. Nurmi, H., Kacprzyk, J. and Fedrizzi, M. (1996). Probabilistic, fuzzy and rough concepts in social choice, Europ. J. of Operational Research, 95, 264-277.
79. Roubens, M. and Vincke, Ph. (1985). Preference Modelling, Springer-Verlag, Berlin.
80. Salles, M. (1996). Fuzzy utility. In S. Barberá, P.J. Hammond and C. Seidl (Eds.): Handbook of Utility Theory, Kluwer, Boston.
81. Sengupta, K. (1999), Choice rules with fuzzy preferences: Some characterizations, Social Choice and Welfare, 16, 259-272.
82. Szmidt, E. and Kacprzyk, J. (1996). Intuitionistic fuzzy sets in group decision making, Notes on Intuitionistic Fuzzy Sets, 2, 15-32.
83. Tanino, T. (1984). Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems, 12, 117-131.
84. Yager, R.R (1988). On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. on Systems, Man and Cybernetics, SMC-18, 183-190.
85. Yager, R.R. and Kacprzyk, J. (Eds.) (1997). The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer, Boston.
86. Zadeh, L.A. (1983). A computational approach to fuzzy quantifiers in natural languages, Computers and Maths. with Appls., 9, 149-184.
87. Zadrozny, S. (1997). An approach to the consensus reaching support in fuzzy environment. In: J. Kacprzyk, H. Nurmi and M. Fedrizzi (Eds.): Consensus under Fuzziness. Kluwer, Boston, pp. 83-109.