Optimization methods to estimate alternatives in AHP: The classification with respect to the dependence of irrelevant alternatives

References

• Altuzarra, A., Moreno-Jiménez, J. M., & Salvador, M. (2007). A Bayesian priorization procedure for AHP-group decision making. European Journal of Operational Research, 182(1), 367–382.10.1016/j.ejor.2006.07.025
   Web of Science ®Google Scholar
• Bajwa, G., Choo, E. U., & Wedley, W. C. (2008). Effectiveness analysis of deriving priority vectors from reciprocal pairwise comparison matrices. Asia-Pacific Journal of Operational Research, 25, 279–299.
   Web of Science ®Google Scholar
• Barzilai, J. (1997). Deriving weights from pairwise comparison matrices. Journal of the Operational Research Society, 48(12), 1226–1232.10.1057/palgrave.jors.2600474
   Web of Science ®Google Scholar
• Blankmeyer, E. (1987). Approaches to consistency adjustment. Journal of Optimization Theory and Applications, 54(3), 479–488.10.1007/BF00940197
   Web of Science ®Google Scholar
• Bozóki, S., & Rapcsák, T. (2008). On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. Journal of Global Optimization, 42(2), 157–175.10.1007/s10898-007-9236-z
   Web of Science ®Google Scholar
• Bryson, N. (1995). A goal programming method for generating priority vectors. Journal of the Operational Research Society, 46(5), 641–648.10.1057/jors.1995.88
   Web of Science ®Google Scholar
• Bryson, N., & Joseph, A. (1999). Generating consensus priority point vectors: A logarithmic goal programming approach. Computers & Operations Research, 26(6), 637–643.10.1016/S0305-0548(98)00083-5
   Web of Science ®Google Scholar
• Chandran, B., Golden, B., & Wasil, E. (2005). Linear programming models for estimating weights in the analytic hierarchy process. Computers & Operations Research, 32, 2235–2254.10.1016/j.cor.2004.02.010
   Web of Science ®Google Scholar
• Choo, E. U., & Wedley, W. C. (2004). A common framework for deriving preference values from pairwise comparison matrices. Computers & Operations Research, 31, 893–908.10.1016/S0305-0548(03)00042-X
   Web of Science ®Google Scholar
• Chu, A. T. W., Kalaba, R. E., & Spingarn, K. (1979). A comparison of two methods for determining the weights of belonging to fuzzy sets. Journal of Optimization Theory and Applications, 27(4), 531–538.10.1007/BF00933438
   Web of Science ®Google Scholar
• Cogger, K. O., & Yu, P. L. (1985). Eigenweight vectors and least-distance approximation for revealed preference in pairwise weight ratios. Journal of Optimization Theory and Applications, 46(4), 483–491.10.1007/BF00939153
   Web of Science ®Google Scholar
• Crawford, G., & Williams, C. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29(4), 387–405.10.1016/0022-2496(85)90002-1
   Web of Science ®Google Scholar
• Deturck, D. M. (1987). The approach to consistency in the analytic hierarchy process. Mathematical Modelling, 9(3-5), 345–352.10.1016/0270-0255(87)90491-X
   Web of Science ®Google Scholar
• Gass, S. I., & Rapcsák, T. (2004). Singular value decomposition in AHP. European Journal of Operational Research, 154(3), 573–584.10.1016/S0377-2217(02)00755-5
   Web of Science ®Google Scholar
• Hochbaum, D. S., & Levin, A. (2006). Methodologies and algorithms for the group-rankings decision. Management Science, 52(9), 1394–1408.10.1287/mnsc.1060.0540
   Web of Science ®Google Scholar
• Ishizaka, A., & Labib, A. (2011). Review of the main developments in the analytic hierarchy process. Expert Systems with Applications, 38(11), 14336–14345.
   Web of Science ®Google Scholar
• Ishizaka, A., & Lusti, M. (2006). How to derive priorities in AHP: A comparative study. Central European Journal of Operations Research, 14(4), 387–400.10.1007/s10100-006-0012-9
   Google Scholar
• Islei, G., & Lockett, A. G. (1988). Judgemental modelling based on geometric least square. European Journal of Operational Research, 36(1), 27–35.10.1016/0377-2217(88)90004-5
   Web of Science ®Google Scholar
• Jensen, B. (1983). Comparisons of eigenvector, least squares, chi square, and logarithmic least squares methods of scaling a reciprocal matrix (Working Paper 127). Trinity University. Retrieved from http://www.trinity.edu/rjensen/127wp/127wp.htm
   Google Scholar
• Johnson, C., Beine, W., & Wang, T. (1979). Right-left asymmetry in an eigenvector ranking procedure. Journal of Mathematical Psychology, 19(1), 61–64.10.1016/0022-2496(79)90005-1
   Web of Science ®Google Scholar
• Kou, G., & Lin, C. (2014). A cosine maximization method for the priority vector derivation in AHP. European Journal of Operational Research, 235(1), 225–232.10.1016/j.ejor.2013.10.019
   Web of Science ®Google Scholar
• Lin, C., Kou, G., & Ergu, D. (2013). A heuristic approach for deriving the priority vector in AHP. Applied Mathematical Modelling, 37(8), 5828–5836.10.1016/j.apm.2012.11.023
   Web of Science ®Google Scholar
• Lundy, M., Siraj, S., & Greco, S. (2017). The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis. European Journal of Operational Research, 257(1), 197–208.10.1016/j.ejor.2016.07.042
   Web of Science ®Google Scholar
• Mikhailov, L. (2000). A fuzzy programming method for deriving priorities in the analytic hierarchy process. Journal of the Operational Research Society, 51(3), 341–349.10.1057/palgrave.jors.2600899
   Web of Science ®Google Scholar
• Raharjo, H., & Endah, D. (2006). Evaluating relationship of consistency ratio and number of alternatives on rank reversal in the AHP. Quality Engineering, 18(1), 39–46.10.1080/08982110500403516
   Google Scholar
• Ramanathan, R. (2006). Data envelopment analysis for weight derivation and aggregation in the analytic hierarchy process. Computers & Operations Research, 33(5), 1289–1307.10.1016/j.cor.2004.09.020
   Web of Science ®Google Scholar
• Saaty, T. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234–281.10.1016/0022-2496(77)90033-5
   Web of Science ®Google Scholar
• Saaty, T. L. (1980). The analytic hierarchy process. New York, NY: McGraw Hill.
   Google Scholar
• Saaty, T. L. (2005). Theory and applications of the analytic network process. Pittsburgh, PA: RWS Publications.
   Google Scholar
• Saaty, T. L., & Vargas, L. G. (1984). Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Mathematical Modelling, 5(5), 309–324.10.1016/0270-0255(84)90008-3
   Web of Science ®Google Scholar
• Schmidt, K., Aumann, I., Hollander, I., & von der Schulenburg, J.-M. G. (2015). Applying the analytic hierarchy process in healthcare research: A systematic literature review and evaluation of reporting. BMC Medical Informatics and Decision Making, 15, 497.10.1186/s12911-015-0234-7
   Web of Science ®Google Scholar
• Siraj, S., Mikhailov, L., & Keane, J. A. (2012). Enumerating all spanning trees for pairwise comparisons. Computers & Operations Research, 39(2), 191–199.10.1016/j.cor.2011.03.010
   Web of Science ®Google Scholar
• Srdjevic, B. (2005). Combining different prioritization methods in the analytic hierarchy process synthesis. Computers & Operations Research, 32(7), 1897–1919.10.1016/j.cor.2003.12.005
   Web of Science ®Google Scholar
• Srdjevic, B., & Srdjevic, Z. (2011). Bi-criteria evolution strategy in estimating weights from the AHP ratio-scale matrices. Applied Mathematics and Computation, 218(4), 1254–1266.10.1016/j.amc.2011.06.006
   Web of Science ®Google Scholar
• Sugihara, K., Ishii, H., & Tanaka, H. (2004). Interval priorities in AHP by interval regression analysis. European Journal of Operational Research, 158(3), 745–754.10.1016/S0377-2217(03)00418-1
   Web of Science ®Google Scholar
• Tsyganok, V. (2010). Investigation of the aggregation effectiveness of expert estimates obtained by the pairwise comparison method. Mathematical and Computer Modelling, 52(3–4), 538–544.10.1016/j.mcm.2010.03.052
   Web of Science ®Google Scholar
• Vaidya, O., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of Operational Research, 169(1), 1–29.10.1016/j.ejor.2004.04.028
   Web of Science ®Google Scholar
• Wang, Y.-M., Fan, Z.-P., & Hua, Z. (2007). A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations. European Journal of Operational Research, 182(1), 356–366.10.1016/j.ejor.2006.07.020
   Web of Science ®Google Scholar
• Wang, Y.-M., & Fu, G. W. (1992). The chi–square priority method of comparison matrix. Journal of Decision and Hierarchy Analytic Process, 2(1), 19–27.
   Google Scholar
• Wang, Y.-M., Parkan, C., & Luo, Y. (2007). Priority estimation in the AHP through maximization of correlation coefficient. Applied Mathematical Modelling, 31(12), 2711–2718.10.1016/j.apm.2006.10.020
   Web of Science ®Google Scholar
• Wang, Y.-M., Parkan, C., & Luo, Y. (2008). A linear programming method for generating the most favorable weights from a pairwise comparison matrix. Computers & Operations Research, 35(12), 3918–3930.10.1016/j.cor.2007.05.002
   Web of Science ®Google Scholar
• Xu, Z. (2004). A weighted least squares method for priorities in AHP. Information, 7(1), 459–468.
   Google Scholar
• Zu, Z. S. (2000). Generalized chi square method for the estimation of weights. Journal of Optimization Theory and Applications, 107(1), 183–192.10.1023/A:1004617102663
   Web of Science ®Google Scholar