A study on the transitivity of probabilistic and fuzzy relations

Fuzzy Sets and Systems

Volumn 184, Issue 1, 2011, Pages 156-170

  Martinetti, D ^a   Montes, I ^a   Diaz S ^a   Montes, S ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Cycle transitivity; Fuzzy relation; Probabilistic relation; Stochastic order; T transitivity

Indexed keywords

CYCLE-TRANSITIVITY; FUZZY RELATION; PROBABILISTIC RELATION; STOCHASTIC ORDER; T-TRANSITIVITY;

RANDOM VARIABLES;

EID: 80052967730     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.06.017     Document Type: Conference Paper

References (31)

1. L. Basile Deleting inconsistencies in nontransitive preference relations Int. J. Intell. Syst. 11 1996 267 277 (Pubitemid 126603419)
2. J. Bezdek, B. Spillman, and R. Spillman A fuzzy relation space for group decision theory Fuzzy Sets Syst. 1 1978 255 268
3. F. Chiclana, E. Herrera-Viedma, S. Alonso, and F. Herrera Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity IEEE Trans. Fuzzy Syst. 17 2009 14 23
4. B. De Baets, and H. De Meyer Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity Fuzzy Sets Syst. 152 2005 249 270 (Pubitemid 40537256)
5. B. De Baets, and H. De Meyer On the cycle-transitive comparison of artificially coupled random variables Int. J. Approx. Reason. 47 2008 306 322
6. B. De Baets, H. De Meyer, and B. De Schuymer Transitive comparison of random variables E.P. Klement, R. Mesiar, Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms 2005 Elsevier 415 442
7. B. De Baets, H. De Meyer, B. De Schuymer, and S. Jenei Cyclic evaluation of transitivity of reciprocal relations Soc. Choice Welfare 26 2006 217 238 (Pubitemid 44030352)
8. H. De Meyer, B. De Baets, and B. De Schuymer On the transitivity of the comonotonic and countermonotonic comparison of random variables J. Multivariate Anal. 98 2007 177 193 (Pubitemid 44567399)
9. B. De Schuymer, H. De Meyer, and B. De Baets Cycle-transitive comparison of independent random variables J. Multivariate Anal. 96 2005 352 373 (Pubitemid 41447904)
10. B. De Schuymer, H. De Meyer, and B. De Baets Extreme copulas and the comparison of ordered lists Theor. Decis. 62 2007 195 217 (Pubitemid 46479903)
11. B. De Schuymer, H. De Meyer, B. De Baets, and S. Jenei On the cycle-transitivity of the dice model Theor. Decis. 54 2003 261 285
12. S. Díaz, B. De Baets, and S. Montes General results on the decomposition of transitive fuzzy relations Fuzzy Optim. Decis. Making 9 2010 1 29
13. S. Díaz, S. Montes, and B. De Baets Transitivity bounds in additive fuzzy preference structures IEEE Trans. Fuzzy Syst. 15 2007 275 286 (Pubitemid 46563427)
14. P.C. Fishburn Binary choice probabilities: on the varieties of stochastic transitivity J. Math. Psychol. 10 1973 327 352
15. E. Herrera-Viedma, S. Alonso, F. Chiclana, and F. Herrera A consensus model for group decision making with incomplete fuzzy preference relations IEEE Trans. Fuzzy Syst. 15 2007 863 877 (Pubitemid 47577994)
16. E. Herrera-Viedma, F. Chiclana, F. Herrera, and S. Alonso Group decision-making model with incomplete fuzzy preference relations based on additive consistency IEEE Trans. Syst. Man Cybern. B 37 2007 176 189 (Pubitemid 46358490)
17. E. Herrera-Viedma, F. Herrera, F. Chiclana, and M. Luque Some issues on consistency of fuzzy preference relations Eur. J. Oper. Res. 154 2004 98 109
18. E. Klement, R. Mesiar, and H. Pap Triangular Norms 2000 Kluwer Academic Publishers Dordrecht
19. H. Levy Stochastic Dominance 1998 Kluwer Academic Publishers Boston
20. R.D. Luce, P. Suppes, Preferences utility and subject probability, in: R.D. Luce, R.R. Bush, E. Galanter (Eds.), Handbook of Mathematical Psychology III, Wiley, 1965, pp. 249-410.
21. B. Monjardet A generalisation of probabilistic consistency: linearity conditions for valued preference relations J. Kacprzyk, M. Roubens, Non-Conventional Preference Relations in Decision Making, Lecture Notes in Economics and Mathematical Systems 1988 Springer 36 53
22. A. Müller, and D. Stoyan Comparison Methods for Stochastic Models and Risk 2002 John Wiley Sons
23. R. Nelsen An Introduction to Copulas, Lecture Notes in Statistics 2006 Springer New York
24. H. Nurmi Approaches to collective decision making with fuzzy preference relations Fuzzy Sets Syst. 6 1981 249 259
25. M. Roubens, and P. Vincke Preference Modelling 1985 Springer Berlin
26. Z. Switalski General transitivity conditions for fuzzy reciprocal preference matrices Fuzzy Sets Syst. 137 2003 85 100
27. T. Tanino Fuzzy preference orderings in group decision making Fuzzy Sets Syst. 12 1984 117 131 (Pubitemid 14569423)
28. T. Tanino Fuzzy preference relations in group decision making J. Kacprzyk, M. Roubens, Lecture Notes in Economics and Mathematical Systems 1988 Springer 54 71
29. T. Tanino On group decision making under fuzzy preferences J. Kacprzyk, M. Fedrizzi, Multiperson Decision Making Using Fuzzy Sets and Possibility Theory 1990 Kluwer Academic Publishers 172 185
30. A. Tversky Intransitivity of preferences Psychol. Rev. 76 1969 31 38
31. B. Van de Walle, B. De Baets, and E. Kerre Characterizable fuzzy preference structures Ann. Oper. Res. 80 1998 105 136