The paper provides mathematical analysis of sensitivity of different combination rules in the DS/AHP method when an alternative is added to the set of decision alternatives while solving foresight problems. Different cases of rank reversals are defined and two sets of conditions for these cases using the method DS/AHP are considered. Rank reversals are illustrated when the DS/AHP method is used to solve practical problem of critical technologies of energy conservation and power efficiency evaluation in Ukraine. It is shown that the DS/AHP method is not sensitive to exclusion (or addition) of an irrelevant decision alternative from (or to) the set of decision alternatives.
References
[1]
M. Z. Zgurovsky and N. D. Pankratova, “System Analysis: Theory and Applications,” Springer, Berlin, 2007.
[2]
T. L. Saaty, “The Analytic Hierarchy Process,” McGraw-Hill, New York, 1980.
[3]
T. L. Saaty, “Theory of the Analytic Hierarchy Process, Part 2.1,” System Research & Information Technologies, No. 1, 2003, pp. 48-72.
[4]
T. L. Saaty, “Theory of the Analytic Hierarchy and Analytic Network Processes—Examples, Part 2.2,” System Research & Information Technologies, No. 2, 2003, pp. 7-34.
[5]
T. L. Saaty, “The Analytic Network Process, Examples, Part 2.3,” System Research & Information Technologies, No. 4, 2003, pp. 7-23.
[6]
N. D. Pankratova and N. I. Nedashkovskaya, “Method for Processing Fuzzy Expert Information in Prediction Problems. Part I,” Journal of Automation and Information Sciences, Vol. 39, No. 3, 2007, pp. 22-36.
doi:10.1615/JAutomatInfScien.v39.i4.30
[7]
N. D. Pankratova and N. I. Nedashkovskaya, “Method for Processing Fuzzy Expert Information in Prediction Problems. Part II,” Journal of Automation and Information Sciences, Vol. 39, No. 6, 2007, pp. 30-44.
doi:10.1615/JAutomatInfScien.v39.i6.20
[8]
M. J. Beynon, B. Curry and P. H. Morgan, “The Dempster-Shafer Theory of Evidence: An Alternative Approach to Multicriteria Decision Modeling,” Omega, Vol. 28, No. 1, 2000, pp. 37-50. doi:10.1016/S0305-0483(99)00033-X
[9]
M. J. Beynon, “DS/AHP Method: A Mathematical Analysis, Including an Understanding of Uncertainty,” European Journal of Operational Research, Vol. 140, No. 1, 2002, pp. 148-164. doi:10.1016/S0377-2217(01)00230-2
[10]
G. Shafer, “A Mathematical Theory of Evidence,” Princeton University Press, Princeton, 1976.
[11]
J. Barzilai and F. A. Lootsma, “Power Relations and Group Aggregation in Multiplicative AHP and SMART,” Proceedings of the 3rd International Symposium on the AHP, Washington DC, 1994, pp.157-168.
[12]
V. Belton and T. Gear, “On a Shortcoming of Saaty’s Method of Analytic Hierarchies,” Omega, Vol. 11, No. 3, 1983, pp. 228-230. doi:10.1016/0305-0483(83)90047-6
[13]
J. S. Dyer, “Remarks on the Analytic Hierarchy Process,” Management Science, Vol. 36, No. 3, 1990, pp. 249-258.
doi:10.1287/mnsc.36.3.249
[14]
E. Triantaphyllou, “Two New Cases of Rank Reversals When the AHP and Some of Its Additive Variants Are Used That Do Not Occur with the Multiplicative AHP,” Journal of Multi-Criteria Decision Analysis, Vol. 10, No. 1, 2001, pp. 11-25. doi:10.1002/mcda.284
[15]
T. L. Saaty, “Rank Generation, Preservation and Reversal in the Analytic Hierarchy Process,” Decision Sciences, Vol. 18, No. 2, 1987, pp. 157-177.
doi:10.1111/j.1540-5915.1987.tb01514.x
[16]
T. L. Saaty, “Rank from Comparisons and from Ratings in the Analytic Hierarchy/ Network Processes,” European Journal of Operational Research, Vol. 168, No. 2, 2006, pp. 557-570. doi:10.1016/j.ejor.2004.04.032
[17]
X. Wang and E. Triantaphyllou, “Ranking Irregularities When Evaluating Alternatives by Using Some ELECTRE Methods,” Omega, Vol. 36, No. 1, 2008, pp. 45-63.
doi:10.1016/j.omega.2005.12.003
[18]
V. G. Totsenko, “On Problem of Reversal of Alternatives Ranks While Multicriteria Estimating,” Journal of Automation and Information Sciences, Vol. 38, No. 6, 2006, pp. 1-11. doi:10.1615/J Automat Inf Scien.v38.i6.10
[19]
M. J. Beynon, “The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule within Group Decision Making,” Group Decision and Negotiation, Vol. 15, No. 1, 2006, pp. 21-42.
doi:10.1007/s10726-005-1159-9
[20]
R. Yager, “On the Dempster-Shafer Framework and New Combination Rules,” Information Sciences, Vol. 41, No. 2, 1987, pp. 93-137. doi:10.1016/0020-0255(87)90007-7
[21]
L. Zhang, “Representation, Independence, and Combination of Evidence in the Dempster-Shafer Theory,” In: R. R. Yager, J. Kacprzyk and M. Fedrizzi, Eds., Advances in the Dempster-Shafer Theory of Evidence, John Wiley & Sons, Inc., New York, 1994, pp. 51-69.
[22]
D. Dubois and H. Prade, “A Set-Theoretic View on Belief Functions: Logical Operations and Approximations by Fuzzy Sets,” International Journal of General Systems, Vol. 12, No. 3, 1986, pp. 193-226.
doi:10.1080/03081078608934937
[23]
N. I. Nedashkovskaya, “Multi-Criteria Decision Making in the Presence of Ignorance Using the DS/AHP Method,” Proceedings of the 11th International Symposium for the AHP/ANP (ISAHP), Naples, 15-18 June 2011.
http://www.isahp.org/italy2011/proceedings-from-past-meetings
