Abstract
The Analytic Hierarchy Process (AHP) method was introduced to help the decision maker to express judgments on alternatives over a number of criteria. In this paper, our proposal extends the AHP method to an uncertain environment, where the uncertainty is represented through the Transferable Belief Model (TBM), one interpretation of the belief function theory. In fact, we suggest a novel framework that tackles the challenge of introducing uncertainty in both the criterion and the alternative levels, where the objective is to represent imperfection that may appear in the pair-wise comparisons and to model the relationship between these alternatives and criteria through conditional beliefs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Beynon, M., Curry, B., Morgan, P.: The Dempster-Shafer theory of evidence: An alternative approach to multicriteria decision modelling. Omega 28(1), 37–50 (2000)
Brans, J.P., Vincke, P., Marechal, B.: How to select and how to rank projects: The PROMOTEE method. European Journal of Operational Research 24, 228–238 (1986)
Dezert, J., Tacnet, J.M., Batton-Hubert, M., Smarandache, F.: Multi-Criteria Decision Making based on DSmT-AHP. In: Workshop on the Theory of Belief Functions (2010)
Ennaceur, A., Elouedi, Z., Lefevre, E.: Handling Partial Preferences in the Belief AHP Method: Application to Life Cycle Assessment. In: Pirrone, R., Sorbello, F. (eds.) AI*IA 2011. LNCS (LNAI), vol. 6934, pp. 395–400. Springer, Heidelberg (2011)
Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: state of the art surveys. Springers International Series in Operations Research and Management Science, vol. 4 (2005)
Keeney, R.L., Raiffa, H.: Decisions with multiple objectives: Preferences and value tradeoffs. Cambridge University Press (1976)
Laarhoven, P.V., Pedrycz, W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems 11, 199–227 (1983)
Saaty, T.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 234–281 (1977)
Saaty, T.: The Analytic Hierarchy Process. McGraw-Hill, New-York (1980)
Schoner, B., Wedley, W.C.: Ambiguous criteria weights in AHP: consequences and solutions. Decision Sciences 20, 462–475 (1989)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)
Smets, P.: Belief functions: the disjunctive rule of combination and the generalized bayesian theorem. International Journal of Approximate Reasoning 9, 1–35 (1993)
Smets, P.: The combination of evidence in the Transferable Belief Model. IEEE Pattern Analysis and Machine Intelligence, 447–458 (1990)
Smets, P., Kennes, R.: The Transferable Belief Model. Artificial Intelligence 66, 191–234 (1994)
Triantaphyllou, E.: Multi-Criteria Decision Making methods: a comparative study. Kluwer Academic Publishers (2000)
Utkin, L.V.: A new ranking procedure by incomplete pairwise comparisons using preference subsets. Intelligent Data Analysis 13(2), 229–241 (2009)
Zeleny, M.: Multiple Criteria Decision Making. McGraw-Hill Book Company (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ennaceur, A., Elouedi, Z., Lefevre, E. (2012). Reasoning under Uncertainty in the AHP Method Using the Belief Function Theory. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-31724-8_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31723-1
Online ISBN: 978-3-642-31724-8
eBook Packages: Computer ScienceComputer Science (R0)