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A ranking model in uncertain, imprecise and multi-experts contexts: the application of evidence theory. (English) Zbl 1226.68109

Summary: We consider ranking problems where the actions are evaluated on a set of ordinal criteria. The evaluation of each alternative with respect to each criterion may be imperfect and is provided by one or several experts. We model each imperfect evaluation as a basic belief assignment (BBA). In order to rank the BBAs characterizing the performances of the actions according to each criterion, a new concept called RBBD and based on the comparison of these BBAs to ideal or nadir BBAs is proposed. This is performed using belief distances that measure the dissimilarity of each BBA to the ideal or nadir BBAs. A model inspired by the method of X. Xu, J. M. Martel and B. F. Lamond [Eur. J. Oper. Res. 133, No. 1, 69–80 (2001; Zbl 0989.90097)] is also proposed and illustrated by a pedagogical example.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
90B50 Management decision making, including multiple objectives

Citations:

Zbl 0989.90097
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References:

[1] Beynon, M.; Cosker, D.; Marshall, D., An expert system for multicriteria decision making using Dempster Shafer theory, Expert Systems with Applications, 20, 357-367 (2001)
[2] Beynon, M.; Curry, B.; Morgan, P., The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling, Omega, 28, 37-50 (2000)
[3] Beynon, M., DS/AHP method: a mathematical analysis including an understanding of uncertainty, European Journal of Operational Research, 140, 148-164 (2002) · Zbl 1012.90017
[4] Boujelben, M. A.; De Smet, Y.; Frikha, A.; Chabchoub, H., Building a binary outranking relation in uncertain, imprecise and multi-experts contexts: the application of evidence theory, International Journal of Approximate Reasoning, 50, 1259-1278 (2009) · Zbl 1186.91059
[5] Boujelben, M. A.; De Smet, Y.; Frikha, A.; Chabchoub, H., DISSET: a disjunctive sorting method based on evidence theory, Foundations of Computing and Decision Sciences, 32, 253-274 (2007)
[6] M.A. Boujelben, Y. De Smet, A. Frikha, H. Chabchoub, The first belief dominance: a new approach in evidence theory for comparing basic belief assignments, in: F. Rossi, A. Tsoukis (Eds.), Lecture Notes in Artificial Intelligence, 2009, pp. 272-283.; M.A. Boujelben, Y. De Smet, A. Frikha, H. Chabchoub, The first belief dominance: a new approach in evidence theory for comparing basic belief assignments, in: F. Rossi, A. Tsoukis (Eds.), Lecture Notes in Artificial Intelligence, 2009, pp. 272-283. · Zbl 1260.91050
[7] Dempster, A. P., Upper and lower probabilities induced by a multi-valued mapping, Annual Mathematics and Statistics, 38, 325-339 (1967) · Zbl 0168.17501
[8] Denoeux, T., Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence, Artificial Intelligence, 172, 234-264 (2008) · Zbl 1182.68298
[9] Denoeux, T., Extending stochastic ordering to belief functions on the real line, Information Sciences, 179, 1362-1376 (2009) · Zbl 1171.68044
[10] Denoeux, T.; Smets, Ph., Classification using belief functions: the relationship between the case-based and model-based approaches, IEEE Transactions on Systems, Man and Cybernetics B, 36, 1395-1406 (2006)
[11] Dubois, D.; Prade, H., Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4, 244-264 (1988)
[12] Ha-Duong, M., Hierarchical fusion of expert opinions in the transferable belief model: application to climate sensitivity, International Journal of Approximate Reasoning, 49, 555-574 (2008)
[13] Hwang, C. L.; Yoon, K. S., Multiple Attribute Decision Making: Methods and Applications (1981), Springer: Springer New York
[14] Jabeur, K.; Martel, J. M.; Khélifa, Ben S., A distance-based collective pre-order integrating the relative importance of the group’s members, Group Decision and Negotiation, 13, 327-349 (2004)
[15] Jousselme, A. L.; Grenier, D.; Bossé, E., A new distance between two bodies of evidence, Information Fusion, 2, 91-101 (2001)
[16] Ristic, B.; Smets, Ph., The TBMglobal distance measure for the association of uncertain combat ID declarations, Information Fusion, 7, 276-284 (2006)
[17] Roy, B., Méthodologie Multicritère d’Aide à la Décision (1985), Economica: Economica Paris
[18] Shafer, G., A Mathematical Theory of Evidence (1976), Princeton University Press: Princeton University Press Princeton · Zbl 0359.62002
[19] Smets, Ph., Analyzing the combination of conflicting belief functions, Information Fusion, 8, 387-412 (2007)
[20] Smets, Ph.; Kennes, R., The transferable belief model, Artificial Intelligence, 66, 191-234 (1994) · Zbl 0807.68087
[21] Smets, Ph., The canonical decomposition of a weighted belief, (Int. Joint Conf. on Artificial Intelligence (1995), Morgan Kaufman: Morgan Kaufman San Mateo, CA), 1896-1901
[22] Tessem, B., Approximations for efficient computation in the theory of evidence, Artificial Intelligence, 61, 315-329 (1993)
[23] Utkin, L. V., A new ranking procedure by incomplete pairwise comparisons using preference subsets, Intelligent Data Analysis, 13, 229-241 (2009)
[24] Utkin, L. V., Ranking procedures by pairwise comparison using random sets and the imprecise Dirichlet model, Applied Mathematics and Computations, 183, 394-408 (2006) · Zbl 1119.65009
[25] Wu, W. Z., Attribute reduction based on evidence theory in incomplete decision systems, Information Sciences, 178, 1355-1371 (2008) · Zbl 1134.68056
[26] Xu, X.; Martel, J. M.; Lamond, B. F., A multiple criteria ranking procedure based on distance between partial preorders, European Journal of Operational Research, 133, 69-80 (2001) · Zbl 0989.90097
[27] Yager, R. R., On the Dempster-Shafer framework and new combination rules, Information Sciences, 41, 93-137 (1987) · Zbl 0629.68092
[28] Yager, R. R., On the relationships of methods of aggregation of evidence in expert systems, Cybernetics and Systems, 16, 1-21 (1985) · Zbl 0583.68049
[29] Yang, J. B.; Singh, M. G., An evidential reasoning approach for multiattribute decision making with uncertainty, IEEE Transactions on Systems, Man and Cybernetics, 24, 1-18 (1994)
[30] Yang, J. B.; Xu, D. L., Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty, IEEE Transactions on Systems, Man and Cybernetics Part A: Systems and Humans, 32, 376-393 (2002)
[31] Yang, J. B.; Xu, D. L., On the evidential reasoning algorithm for multiattribute decision analysis under uncertainty, IEEE Transactions on Systems, Man and Cybernetics Part A: Systems and Humans, 32, 289-304 (2002)
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