A Hierarchical Decision Model Based on Pairwise Comparisons

• Autorzy: Hou F.

Identyfikatory

DOI

10.3233/FI-2016-1339

• Języki publikacji: EN

Abstrakty

EN

Pairwise comparisons (PC) method is an efficient technique and hierarchical analysis is a popular means coping with complex decision problems. Based on two proposed theorems, this paper shows that the PC-based hierarchical decision models stem from the weighted average methods (including the arithmetic form and the geometric form). Some issues (including the rank reversal, the criterion for acceptable consistency and the method for deriving priorities, etc) associated with the current PC-based hierarchical models (including the AHP, the multiplicative AHP and the FPR-AHP) are investigated. Another PC-based hierarchical decision model, which is different from the Saaty’s AHP, is introduced for applications by virtue of its desirable traits (such as the rank preservation, the isomorphic correspondence, etc).

Słowa kluczowe

EN

hierarchical decision model; weighted average method; pairwise comparison matrix; PCM; fuzzy preference relations; FPR; isomorphic correspondence

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 144, nr 3/4
• Strony: 333--348
• Opis fizyczny: Bibliogr. 45 poz., rys., tab.

Twórcy

autor

Hou F.

• School of Management and Economics, Beijing Institute of Technology, Beijing 100081, P.R. China

Bibliografia

• [1] Janicki R, Koczkodaj WW. A weak order solution to a group ranking and consistency-driven pairwise comparisons. AppliedMathematics and Computation. 1998;94(2):227–241. doi:10.1016/S0096-3003(97)10080-7.
• [2] Janicki R. Pairwise comparisons based non-numerical ranking. Fundamenta Informaticae. 2009;94(2):197–217. doi:10.3233/FI-2009-126.
• [3] Janicki R, Zhai Y. Remarks on pairwise comparison numerical and non-numerical rankings. In: Rough Sets and Knowledge Technology. vol. 6954 of LNCS. Springer Berlin Heidelberg; 2011. p. 290–300. doi:10.1007/978-3-642-24425-4 39.
• [4] Saaty TL. The Analytic Hierarchy Process. New york: McGraw-Hill; 1980.
• [5] Tanino T. Fuzzy preference orderings in group decision making. Fuzzy sets and systems. 1984;12(2):117–131. doi:10.1016/0165-0114(84)90032-0.
• [6] Triantaphyllou E, Mann SH. Using the analytic hierarchy process for decision making in engineering applications: some challenges. International Journal of Industrial Engineering: Applications and Practice. 1995;2(1):35–44.
• [7] Tanino T. Fuzzy preference relations in group decision making. vol. 301 of Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg; 1988. doi:10.1007/978-3-642-51711-2 4.
• [8] Donegan HA, Dodd FJ, McMaster TBM. A new approach to AHP decision-making. Journal of the Royal Statistical Society Series D: The Statistician. 1992;41(3):295–302. Available from: http://www.jstor.org/stable/2348551. doi:10.2307/2348551.
• [9] Schoner B, Wedley WC. Ambiguous Criteria Weights in AHP: Consequences and Solutions. Decision Sciences. 1989;20(3):462–475. doi:10.1111/j.1540-5915.1989.tb01561.x.
• [10] Schoner B, Wedley WC, Choo EU. A unified approach to AHP with linking pins. European Journal of Operational Research. 1993;64(3):384–392. doi:10.1016/0377-2217(93)90128-A.
• [11] Barzilai J, Cook WD, Golani B. Consistent weights for judgement matrices of the relative importance of alternatives. Operations Research Letters. 1987;6(3):131–134. doi:10.1016/0167-6377(87)90026-5.
• [12] Barzilai J, Golany B. An axiomatic framework for aggregating weights and weight-ratio matrices. In: Proceedings of the Second International Symposium on the AHP. Pittsburgh, Pennsylvania; 1992. p. 59–70.
• [13] Lootsma FA. Numerical scaling of human judgement in pairwise comparison methods for fuzzy multi-criteria decision analysis. vol. 48 of NATO ASI Series. Springer Berlin Heidelberg; 1988. doi:10.1007/978-3-642-83555-1 3.
• [14] Lootsma FA. Scale sensitivity in the Multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis. 1993;2(2):87–110. doi:10.1002/mcda.4020020205.
• [15] Olson DL, Fliedner G, Currie K. Comparison of the REMBRANDT system with analytic hierarchy process. European Journal of Operational Research. 1995;82(3):522–539. doi:10.1016/0377-2217(93)E0340-4.
• [16] Chang TH, Wang TC. Measuring the success possibility of implementing advanced manufacturing technology by utilizing the consistent fuzzy preference relations. Expert Systems with Applications. 2009; 36(3):4313–4320. doi:10.1016/j.eswa.2008.03.019.
• [17] Chao RJ, Chen YH. Evaluation of the criteria and effectiveness of distance elearning with consistent fuzzy preference relations. Expert Systems with Applications. 2009;36(7):10657–10662. doi:10.1016/j.eswa.2009.02.047.
• [18] Wang TC, Chen YH. Applying consistent fuzzy preference relations to partnership selection. Omega. 2007;35(4):384–388. doi:10.1016/j.omega.2005.07.007.
• [19] Belton V, Gear T. On a shortcoming of Saaty’s method of analytic hierarchies. Omega. 1983;11(3):228–230. doi:10.1016/0305-0483(83)90047-6.
• [20] Dyer JS. Remarks on the analytic hierarchy process. Management Science. 1990;36(6):249–258. Available from: http://www.jstor.org/stable/2631946.
• [21] Saaty TL, Vargas LG. The legitimacy of rank reversal. Omega. 1984;12(5):513–516. doi:10.1016/0305-0483(84)90052-5.
• [22] Johnson CR, Beine WB, Wang TJ. Right-left asymmetry in an eigenvector ranking procedure. Journal of Mathematical Psychology. 1979;19(9):61–64. doi:10.1016/0022-2496(79)90005-1.
• [23] Barzilai J. Deriving weights from pairwise comparison matrices. Journal of the Operational Research Society. 1997;48(12):1226–1232. Available from: http://www.jstor.org/stable/3010752. doi:10.2307/3010752.
• [24] e Costa CAB, Vansnick JC. A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research. 2008;187(3):1422–1428. doi:10.1016/j.ejor.2006.09.022.
• [25] Barzilai J, Golany B. Deriving weights from pairwise comparison matrices: The additive case. Operations Research Letters. 1990;9(6):407–410. doi:10.1016/0167-6377(90)90062-A.
• [26] Lootsma FA. A model for the relative importance of the criteria in the Multiplicative AHP and SMART. European Journal of Operational Research. 1996;94(3):467–476. doi:10.1016/0377-2217(95)00129-8.
• [27] Saaty TL, Vargas LG. The analytic hierarchy process: Wash criteria should not be ignored. International Journal of Management and Decision Making. 2006;7(2):180–188. doi:10.1504/IJMDM.2006.009142.
• [28] Fedrizzi M, Brunelli M. On the normalisation of a priority vector associated with a reciprocal relation. International Journal of General Systems. 2009;38(5):579–586. doi:10.1080/03081070902753606.
• [29] Barzilai J, Golany B. AHP rank reversal, normalization and aggregation rules. INFOR. 1994;32(2):57–64. Available from: http://hdl.handle.net/10222/43855.
• [30] Hou F. A Semiring-based study of judgment matrices: properties and models. Information Sciences. 2011;181(11):2166–2176. doi:10.1016/j.ins.2011.01.020.
• [31] Hou F. Rank preserved aggregation rules and application to reliability allocation. Communications in Statistics - Theory and Methods. 2012;41(21):3831–3845. doi:10.1080/03610926.2012.688156.
• [32] Hou F. A semiring-based hierarchical decision model and application. Journal of Data Analysis and Operations Research. 2014;1(1):25–33.
• [33] van Laarhoven PJM, Pedrycz W. A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems. 1983;11(1):229–241. doi:10.1016/S0165-0114(83)80082-7.
• [34] Saaty TL. There is no mathematical validity for using fuzzy number crunching in the Analytic Hierarchy Process. Journal of Systems Science and Systems Engineering. 2006;15(4):457–464. doi:10.1007/s11518-006-5021-7.
• [35] Saaty TLT T L. On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process. Mathematical and Computer Modelling. 2007;46(7-8):962–975. doi:10.1016/j.mcm.2007.03.022.
• [36] Thurstone LL. A law of comparative judgements. Psychological Review. 1927;34(4):273–286. doi:http://dx.doi.org/10.1037/h0070288.
• [37] Miller III JR. The assessment of worth: a systematic procedure and its experimental validation. Massachusetts Institute of Technology; 1966. Available from: http://hdl.handle.net/1721.1/13513.
• [38] Jensen RE. An alternative scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology. 1984;28(3):317–332. doi:10.1016/0022-2496(84)90003-8.
• [39] Dejong P. A statistical approach to saaty scaling method for priorities. Journal of Mathematical Psychology. 1984;28(4):467–478. doi:10.1016/0022-2496(84)90013-0.
• [40] Crawford G, Williams C. A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology. 1985;29(4):387–405. doi:10.1016/0022-2496(85)90002-1.
• [41] Fedrizzi M. On a consensus measure in a group MCDM problem. vol. 18 of Theory and Decision Library. Springer Netherlands; 1990. doi:10.1007/978-94-009-2109-2 20.
• [42] Chiclana F, Herrera F, Herrera-Viedma E. Integrating multiplicative preference relation in a multipurpose decision making model based on fuzzy preference relations. Fuzzy Sets and Systems. 2001;122(2):277–291. doi:10.1016/S0165-0114(00)00004-X.
• [43] Herrera-Viedma E, Herrera F, Chiclana F, LuqueM. Some issues on consistency of fuzzy preference relations. European Journal of Operational Research. 2004;154(1):98–109. doi:10.1016/S0377-2217(02)00725-7.
• [44] Barzilai J. Consistency measures for pairwise comparison matrices. Journal of Multi-Criteria Decision Analysis. 1998;7(3):123–132. doi:10.1002/(SICI)1099-1360(199805)7:3<123::AID-MCDA181>3.0.CO;2-8.
• [45] Elsner L, van den Driessche P. Max-algebra and pairwise comparison matrices. Linear Algebra and its Applications. 2004;385:47–62. doi:10.1016/S0024-3795(03)00476-2.