Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression

Omega (United Kingdom)

Volumn 61, Issue , 2016, Pages 2-18

  Corrente, Salvatore ^a   Greco, Salvatore ^a,b   Ishizaka, Alessio ^b  

^a University of Catania and CESifo Research Network   (Italy)

^b UNIVERSITY OF PORTSMOUTH   (United Kingdom)

Author keywords

Analytical hierarchy process; Choquet integral; Interaction between criteria; Multiple criteria decision aiding; Non additive robust ordinal regression

Indexed keywords

DECISION SUPPORT SYSTEMS; FUNCTION EVALUATION; HIERARCHICAL SYSTEMS; INTEGRAL EQUATIONS; REGRESSION ANALYSIS;

ANALYTICAL HIERARCHY PROCESS; CHOQUET INTEGRAL; COMPLEX FORMULATIONS; INTERACTION BETWEEN CRITERION; MULTIPLE CRITERIA DECISION AIDING; NON-ADDITIVE ROBUST ORDINAL REGRESSIONS; PREFERENCE INFORMATION; REFERENCE POINTS; VALUE FUNCTIONS; WEIGHTED SUM;

ANALYTIC HIERARCHY PROCESS;

EID: 84940705819     PISSN: 03050483     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.omega.2015.07.003     Document Type: Article

References (66)

1. Angilella S., Corrente S., Greco S. Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem. European Journal of Operational Research 2015, 240:172-182.
2. Angilella S., Greco S., Lamantia F., Matarazzo B. Assessing non-additive utility for multicriteria decision aid. European Journal of Operational Research 2004, 158(3):734-744.
3. Angilella S, Greco S, Matarazzo B. The most representative utility function for non-additive robust ordinal regression. In: Hullermeier E, Kruse R, Hoffmann F, editors, Proceedings of IPMU 2010, LNAI 6178, Springer, Heidelberg; 2010. p. 220-29.
4. Angilella S., Greco S., Matarazzo B. Non-additive robust ordinal regression. a multiple criteria decision model based on the Choquet integral. European Journal of Operational Research 2010, 201(1):277-288.
5. Bana e Costa C., Vansnick J.-C. MACBETH-an interactive path towards the construction of cardinal value functions. International Transactions in Operational Research 1994, 1(4):489-500.
6. Bana e Costa C., Vansnick J.-C. A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research 2008, 187(3):1422-1428.
7. Bell D.E. Multiattribute utility functions. decompositions using interpolation. Management Science 1979, 25:744-753.
8. Berrah L., Clivillé V. Towards an aggregation performance measurement system model in a supply chain context. Computers in Industry 2007, 58(7):709-719.
9. Bortot S., Marques Pereira R.A. Inconsistency and non-additive capacities. the analytic hierarchy process in the framework of Choquet integration. Fuzzy Sets and Systems 2013, 213:6-26.
10. Boutilier C, Bacchus F, Brafman RI. UCP-networks: a directed graphical representation of conditional utilities. In: Proceedings of the seventeenth conference on uncertainty in artificial intelligence, Morgan Kaufmann Publishers Inc.; 2001. p. 56-64.
11. Brans J.P., Mareschal B. PROMETHEE methods. Multiple criteria decision analysis: state of the art surveys 2005, 163-196. Springer, Berlin. J. Figueira, S. Greco, M. Ehrgott (Eds.).
12. Brans J.P., Vincke Ph. A preference ranking organisation method. the PROMETHEE method for MCDM. Management Science 1985, 31(6):647-656.
13. Chateauneuf A., Jaffray J.Y. Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Mathematical Social Sciences 1989, 17:263-283.
14. Choquet G. Theory of capacities. Annales de l[U+05F3]institut Fourier 1954, 5:131-295.
15. Corrente S., Figueira J.R., Greco S. Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE methods. Annals of Operations Research 2014, 217(1):137-164.
16. Corrente S., Greco S., Kadziński M., Słowiński R. Robust ordinal regression in preference learning and ranking. Machine Learning 2013, 93:381-422.
17. Corrente S., Greco S., Kadziński M., Słowiński R. Robust ordinal regression. Wiley Encyclopedia of Operational Research 2014, 1-10.
18. Elliott M. Selecting numerical scales for pairwise comparisons. Reliability Engineering and System Safety 2010, 95(7):750-763.
19. Farquhar P.H. A fractional hypercube decomposition theorem for multiattribute utility functions. Operations Research 1975, 23:941-967.
20. Figueira J., Greco S., Ehrgott M. Multiple criteria decision analysis. state of the art surveys 2005, Springer, Berlin.
21. Figueira J., Greco S., Roy B., Słowiński R. An overview of ELECTRE methods and their recent extensions. Journal of Multicriteria Decision Analysis 2013, 20:61-85.
22. Figueira J, Greco S, Słowiński R. Identifying the most representative value function among all compatible value functions in the GRIP. In: Proceedings of the 68th EURO Working Group on MCDA, Chania, October 2008.
23. Figueira J., Mousseau V., Roy B. ELECTRE methods. Multiple criteria decision analysis: state of the art surveys 2005, 133-153. Springer, Berlin. J. Figueira, S. Greco, M. Ehrgott (Eds.).
24. Figueira J.R., Greco S., Roy B. ELECTRE methods with interaction between criteria. an extension of the concordance index. European Journal of Operational Research 2009, 199(2):478-495.
25. Fishburn P.C. Utility theory for decision making 1970, Wiley, New York.
26. Fishburn P.C., Keeney R.L. Generalized utility independence and some implications. Operations Research 1975, 23:928-940.
27. Giarlotta A., Greco S. Necessary and possible preference structures. Journal of Mathematical Economics 2013, 49(2):163-172.
28. Gigerenzer G., Gaissmaier W. Heuristic decision making. Annual Review of Psychology 2011, 62:451-482.
29. Gilboa I., Schmeidler D. Additive representations of non-additive measures and the Choquet integral. Annals of Operations Research 1994, 52:43-65.
30. Gonzales C, Perny P. GAI networks for utility elicitation. In: Proceedings of the ninth international conference on the principles of knowledge representation and reasoning. CA: AAAI Press; 2004. p. 223-34.
31. Grabisch.M. The application of fuzzy integrals in multicriteria decision making. European Journal of Operational Research 1996, 89:445-456.
32. Grabisch M. k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 1997, 92:167-189.
33. Grabisch M., Kojadinovic I., Meyer P. A review of methods for capacity identification in Choquet integral based multi-attribute utility theory. applications of the kappa lab R package. European Journal of Operational Research 2008, 186(2):766-785.
34. Grabisch M., Labreuche C. Bi-capacities-Part I. definition, Möbius transform and interaction. Fuzzy Sets and Systems 2005, 151(2):211-236.
35. Grabisch M., Labreuche C. A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 2008, 6(1):1-44.
36. Greco S., Matarazzo B., Giove.S. The Choquet integral with respect to a level dependent capacity. Fuzzy Sets and Systems 2011, 175(1):1-35.
37. Greco S., Mousseau V., Słowiński R. Ordinal regression revisited. multiple criteria ranking using a set of additive value functions. European Journal of Operational Research 2008, 191(2):416-436.
38. Greco S., Mousseau V., Słowiński R. Robust ordinal regression for value functions handling interacting criteria. European Journal of Operational Research 2014, 239(3):711-730.
39. Ishizaka A., Balkenborg D., Kaplan T. Does AHP help us make a choice? An experimental evaluation. Journal of the Operational Research Society 2011, 62(10):1801-1812.
40. Ishizaka A., Labib.A. Analystic hierarchy process and expert choice. benefits and limitations. OR Insight 2009, 22(4):201-220.
41. Ishizaka A., Lusti M. How to derive priorities in AHP. a comparative study. Central European Journal of Operations Research 2006, 14(4):387-400.
42. Ishizaka A., Nemery P. Multicriteria decision aid. methods and software 2013, Wiley, Chichester.
43. Ishizaka A., Nguyen N.H. Calibrated fuzzy AHP for current bank account selection. Expert Systems with Applications 2013, 40(9):3775-3783.
44. Keeney R.L. Analysis of preference dependencies among objectives. Operations Research 1981, 29:1105-1120.
45. Keeney R.L., Raiffa H. Decisions with multiple objectives. preferences and value tradeoffs 1993, J. Wiley, New York.
46. Marichal J.L., Roubens M. Determination of weights of interacting criteria from a reference set. European Journal of Operational Research 2000, 124(3):641-650.
47. Miller.G.A. The magical number seven, plus or minus two. some limits on our capacity for processing information. Psychological Review 1956, 63(2):81.
48. Millet I. The effectiveness of alternative preference elicitation methods in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis 1997, 6(1):41-51.
49. Mousseau V., Figueira J., Dias L., Gomes da Silva C., Climaco J. Resolving inconsistencies among constraints on the parameters of an MCDA model. European Journal of Operational Research 2003, 147(1):72-93.
50. Murofushi S, Soneda T. Techniques for reading fuzzy measures (III): interaction index. In: 9th Fuzzy Systems Symposium, Sapporo, Japan; 1993. p. 693-96.
51. Pérez J., Jimeno J.L., Mokotoff E. Another potential shortcoming of AHP. Top 2006, 14(1):99-111.
52. Rokou E., Kirytopoulos K. A calibrated group decision process. Group Decision and Negotiation 2014, 23(6):1369-1384.
53. Rota G.C. On the foundations of combinatorial theory I. Theory of Möbius functions. Wahrscheinlichkeitstheorie und Verwandte Gebiete 1964, 2:340-368.
54. Roy B, Bouyssou D. Aide multicritère à la décision: méthodes et cas. Economica; 1993.
55. Saaty.T. A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 1977, 15(3):234-281.
56. Saaty T. The analytic hierarchy process 1980, McGraw-Hill, New York.
57. Saaty T. How to make a decision. the analytic hierarchy process. European Journal of Operational Research 1990, 48(1):9-26.
58. Saaty T. Decision making with dependence and feedback. the analytic network process 1996, RWS Publications, Pittsburgh.
59. Saaty T.L., Ozdemir M.S. Why the magic number seven plus or minus two. Mathematical and Computer Modelling 2003, 38(3):233-244.
60. Salo A., Hämäläinen R.P. On the measurement of preferences in the analytic hierarchy process. Journal of Multi-criteria Decision Analysis 1997, 6(6):309-319.
61. Shafer G. A mathematical theory of evidence 1976, Princeton University Press, Princeton NJ.
62. Shapley L.S. A value for n-person games. Contributions to the theory of games II 1953, 307-317. Princeton University Press, Princeton. H.W. Kuhn, A.W. Tucker (Eds.).
63. Sugeno M. Theory of fuzzy integrals and its applications. PhD thesis 1974, Tokyo Institute of Technology, Japan.
64. Wakker P.P. Additive representations of preferences: a new foundation of decision analysis 1989, vol. 4. Springer, Berlin.
65. Wang Y.-M., Chin K.-S., Luo Y. Aggregation of direct and indirect judgments in pairwise comparison matrices with a re-examination of the criticisms by Bana e Costa and Vansnick. Information Sciences 2009, 179(3):329-337.
66. Wu J.-Z., Zhang Q. 2-order additive fuzzy measure identification method based on diamond pairwise comparison and maximum entropy principle. Fuzzy Optimization and Decision Making 2010, 9(4):435-453.