Preference structures and co-comparability graphs

Journal of Multi-Criteria Decision Analysis

Volumn 5, Issue 2, 1996, Pages 81-98

  Abbas, Moncef ^a,b   Pirlot, Marc ^c   Vincke, Philippe ^b  

^a UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c FACULTÉ POLYTECHNIQUE DE MONS   (Belgium)

Author keywords

Comparability graphs; Order; Perfect graphs; Preference modelling

Indexed keywords

EID: 21844441459     PISSN: 10579214     EISSN: 10991360     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1360(199606)5:2<81::AID-MCDA101>3.0.CO;2-V     Document Type: Article

References (36)

1. Abbas, M., ‘Contribution au rapprochement de la théorie des graphes et de l’aide à la décision: graphes parfaits et modèles de préférence’, Thèse de Doctorat, Université Libre de Bruxelles, 1994.
2. Abbas, M., and Vincke, Ph., ‘Preference structures and threshold models’, J. Multi-Crit. Decis. Anal., 2, 171-178(1993).
3. Abbas, M., and Vincke, Ph., ‘A new fundamental preference structure: threshold order’, JORBEL, 1, 1994.
4. Agaev, R., and Aleskerov, F., ‘Interval choice: classical and general cases’, Math. Social Sci., 26, 249-272(1993).
5. Berge, C., and Chvatal, V., ‘Topics on perfect graphs’, Ann. Discrete Math., (1984).
6. Cheah, H. K., ‘A recognition algorithm for II-graph’, Tech. Rep. 246, Department of Computer Science, University of Toronto, 1990.
7. Corneil, D. G., and Kamula, P. A., ‘Extensions of permutation and interval graphs’, Congr. Numer., 58, 267-275(1987).
8. Dagan, I., Golumbic, M. C., and Pinter, R. Y., ‘Trapezoid graphs and their coloring’, Discrete Appl. Math., 21, 35-46(1988).
9. Damaschke, P., ‘Note on: distance in cocomparability graphs and their powers’, Discrete Appl. Math., 35, 67-72(1992).
10. Fishburn, P. C., ‘Intransitive indifference with unequal indifference intervals’, J. Math. Psychol., 7, 144-149(1970).
11. Fishburn, P. C., Interval Orders and Interval Graphs, New York:Wiley, 1985.
12. Gallaï, T., ‘Transitive orienterbare Graphen’, Acta Math. Sci. Hung., 18, 25-66(1967).
13. Ghouïla-Houri, A., ‘Caractérisation des graphes non orientés dont on peut orienter les arètes de manière à obtenir le graphe d’une relation d’ordre’, C. R. Acad. Sci. Paris., 254, 1370-1371(1962).
14. Gilmore, P. C., and Hoffman, A., ‘A characterization of comparability graphs and of interval graphs’, Can. J. Math., 16, 539-548(1964).
15. Golumbic, M. C., ‘The complexity of comparability graph recognition and coloring’, Computing, 18, 199-208(1977).
16. Golumbic, M. C., ‘Note on trivially perfect graphs’, Discrete Math., 24, 105-107(1978).
17. Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs, New York:Academic, 1980.
18. Habib, M., and Möhring, R. H., ‘Recognition of partial orders with interval dimension two via transitive orientation with side constraints’, Prepr. ‘Reihe Math. 244, Technische Universität, Berlin, 1990.
19. Hajös, G., 'Über eine Art von Graphen’, Int. Math. Nachr., 11, Problem 65(1957).
20. Lekkerkerker, C. G., and Boland, J. Ch., ‘Representation of a finite graph by a set of intervals on the real line’, Fund. Math., 51, 45-64(1962).
21. Lerchs, H., ‘On cliques and kernels’, Report, Department of Computer Science, University of Toronto, 1971.
22. Luce, R. D., ‘Semiorders and a theory of utility discrimination’, Econometrica, 24, 178-191.
23. Ribeill, G., ‘Equilibre équivalence, ordre et préordre à distance minimum d’un graphe complet’, Math. Sci. Hum., 43, 71-76(1973).
24. Roberts, F. S., ‘Indifference graphs’, in Harary, F. (ed.), Proof Techniques in Graph Theory, New York:Academic, 1969, pp. 139-146.
25. Roubens, M., and Vincke, Ph., ‘Linear orders and semiorders close to an interval order’, Discrete Appl. Math., 6, 311-314(1983).
26. Roubens, M., and Vincke, Ph., Preference Modelling, Berlin:Springer, 1985.
27. Roy, B., ‘Critères multiples et modélisation des préférences: l’apport des relations de surclassement’, Rev. Econ. Polit., 1, (1974).
28. Roy, B., Méthodologie Multicritère d’Aide à la Décision, Paris:Economica, 1985.
29. Roy, B., and Bouyssou, D., Aide Multicritère à la Décision: Méthodes et Cas, Paris:Economica, 1993.
30. Scott, D., and Suppes, P., ‘Foundational aspects of theories of measurement’, J. Symbol. Logic, 23, 113-128(1958).
31. Vincke, Ph., ‘Ordres et préordres totaux à distance minimum d’un quasi-ordre’, Cah. Centre Etud. Rech. Opér., 20, 3-4(1978).
32. Vincke, Ph., '(P, Q, I)-preferences structures’, in Kacprzyck, J. and Roubens, M. (eds), Non-Conventional Preference Relations in Decision Making, Berlin:Springer, 1988, pp. 72-81.
33. Vincke, Ph., Multicriteria Decision-Aid, Chichester:Wiley, 1992.
34. n, Ph.D. Thesis, Universität Göttingen, 1967.
35. Wolk, E. S., ‘The comparability graph of a tree’, Proc. Am. Math. Soc., 3, 789-795(1962).
36. Wolk, E. S., ‘A note on the comparability graph of a tree’, Proc. Am. Math. Soc., 16, 17-20(1965).