Deriving Weights of the Decision Makers Using AHP Group Consistency Measures

• Autorzy: Blagojevic, B. , Srdjevic, B. , Srdjevic, Z. , Zoranovic, T.
• Języki publikacji: EN

Abstrakty

EN

In AHP group decision making it is desirable that decision makers achieve the highest degree of consensus concerning the group priority vector at both levels, local and the final. Based on this philosophy, we have developed a method to derive local group priority vector respecting the three group consistency measures: geometric cardinal consensus index (GCCI), group minimum violation coefficient (GMV) and ordinal consensus measure (OCM). Consistency of individual decisions against the group decision serves as an input to determine the weights of decision makers participating in the group and generate the group local priority vector. Proposed method rewards cooperation between members of the group and raises chances for their consensus.

Słowa kluczowe

EN

AHP group decision making; weights of decision makers; group consistency measures

• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 144, nr 3/4
• Strony: 383--395
• Opis fizyczny: Bibliogr. 40 poz., tab.

Twórcy

autor

Blagojevic, B.

• University of Novi Sad, Faculty of Agriculture, Department of Water Management, Trg D. Obradovica 8, 21000 Novi Sad, Serbia,

autor

Srdjevic, B.

• University of Novi Sad, Faculty of Agriculture, Department of Water Management, Trg D. Obradovica 8, 21000 Novi Sad, Serbia

autor

Srdjevic, Z.

• University of Novi Sad, Faculty of Agriculture, Department of Water Management, Trg D. Obradovica 8, 21000 Novi Sad, Serbia

autor

Zoranovic, T.

• University of Novi Sad, Faculty of Agriculture, Department of Water Management, Trg D. Obradovica 8, 21000 Novi Sad, Serbia

Bibliografia

• [1] Saaty TL. The Analytical Hierarchy Process. New York: McGraw Hill; 1980. doi:10.1016/0270-0255(87)90473-8.
• [2] Ho W. Integrated analytic hierarchy process and its applications - A literature review. European Journal of Operational Research. 2008;186(1):211–228. doi:10.1016/j.ejor.2007.01.004.
• [3] Subramanian N, Ramanathan R. A review of applications of Analytic Hierarchy Process in operations management. International Journal of Production Economics. 2012;138(2):215–241. doi:10.1016/j.ijpe.2012.03.036.
• [4] Vaidya OS, Kumar S. Analytic hierarchy process: An overview of applications. European Journal of Operational Research. 2006;169(1):1–29. doi:10.1016/j.ejor.2004.04.028.
• [5] Dragincic J BB, Korac N. Group multi-criteria decision making (GMCDM) approach for selecting the most suitable table grape variety intended for organic viticulture. Computers and Electronics in Agriculture. 2015;111(C):194–202. ISSN: 0168-1699. doi:10.1016/j.compag.2014.12.023.
• [6] Srdjevic B, Pipan M, Srdjevic Z, Blagojevic B, Zoranovic T. Virtually combining the analytical hierarchy process and voting methods in order to make group decisions. Universal Access in the Information Society. 2013;14(2):231–245. ISSN:1615-5297. doi:10.1007/s10209-013-0337-9.
• [7] Srdjevic B, Srdjevic B, Blagojevic B, Cukaliev O. Multi-Criteria Evaluation of Groundwater Ponds as Suppliers to Urban Water Distribution Systems. Springer Netherlands; 2014. ISBN:978-94-007-7161-1. doi:10.1007/978-94-007-7161-1 9.
• [8] Srdjevic Z, Srdjevic B, Blagojevic B, Pipan M. Innovative Group Decision Making Framework for Sustainable Management of Regional Hydro-Systems. NATO Science for Peace and Security Series C: Environmental Security. Springer Netherlands; 2014. doi:10.1007/978-94-007-7161-1 7.
• [9] Ramanathan R, Ganesh LS. Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members’ weightages. European Journal of Operational Research. 1994;79(2):249–265. doi:10.1016/0377-2217(94)90356-5.
• [10] Bodily SE. A Delegation Process for Combining Individual Utility Functions. Science. 1979;25(10):1035–1041. Available from: http://www.jstor.org/stable/2630767.
• [11] Lootsma FA. vol. 8 of Applied Optimization. Springer US; 1997. ISBN:978-1-4419-4779-6. doi:10.1007/978-1-4757-2618-3.
• [12] Lootsma FA. vol. 29 of Applied Optimization. Springer US; 1999. ISBN:978-0-585-28008-0. doi:10.1007/b102374.
• [13] Srdjevic Z, Blagojevic B, Srdjevic B. AHP based group decision making in ranking loan applicants for purchasing irrigation equipment: a case study. Bulgarian Journal of Agricultural Science. 2011;17(4):531–543.
• [14] Honer RCVD. Decisional Power in Group Decision Making: A Note on the Allocation of Group Members’ Weights in the Multiplicative AHP and SMART. Decision and Negotiation. 2001;10(3):275–286. ISSN:1572-9907. doi:10.1023/A:1011201501379.
• [15] Xu ZS. Two methods for deriving members’ weights in group decision making. Systems Science and Systems Engineering. 2001;10(1):15–19.
• [16] Xu ZS. Group decision making based on multiple types of linguistic preference relations. Information Sciences. 2008;178(2):452–467. doi:10.1016/j.ins.2007.05.018.
• [17] Chiclana F, Herrera-Viedma E, Herrera F, Alonso S. Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. European Journal of Operational Research. 2007;182(1):383–399. doi:10.1016/j.ejor.2006.08.032.
• [18] Blagojevic B, Srdjevic B, Srdjevic Z, Lakicevic M. Allocation of budget funds on agricultural loan programs: group consensus decision making in the Provincial Fund for Agricultural Development of Vojvodina Province in Serbia. Industrija (Journal of Economics Institute). 2012;40(3):57–70. ISSN: 2334-8526.
• [19] Yue ZL. Developing a straightforward approach for group decision making based on determining weights of decision makers. Applied Mathematical Modelling. 2012;36(9):4106–4117. doi:10.1016/j.apm.2011.11.041.
• [20] Ju YB, Wang AH. Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting. Applied Mathematical Modelling. 2013;37(20-21):9031–9040. doi:10.1016/j.apm.2013.04.027.
• [21] Ju Y. A new method for multiple criteria group decision making with incomplete weight information under linguistic environment. Applied Mathematical Modelling. 2014;38(21-22):5256–5268. doi:10.1016/j.apm.2014.04.022.
• [22] Xu Z, Cai X. Minimizing group discordance optimization model for deriving expert weights. Group Decision and Negotiation. 2012;21(6):863–875. doi:10.1007/s10726-011-9253-7.
• [23] Lehrer K, Wagner C. vol. 24 of Philosophical Studies Series. Springer Netherlands; 1981. ISBN:978-90-277-1307-0. doi:10.1007/978-94-009-8520-9.
• [24] Srdjevic B, Srdjevic Z, Blagojevic B, Suvocarev K. A two-phase algorithm for consensus building in AHP-group decision making. Applied Mathematical Modelling. 2013;37(10-11):6670–6682. doi:10.1016/j.apm.2013.01.028.
• [25] Colyvan HMR, Markovchick-Nicholls L. A formal model for consensus and negotiation in environmental management. Journal of Environmental Management. 2006;80(2):167–176. doi:10.1016/j.jenvman.2005.09.004.
• [26] Dong YC, Zhang GQ, Hong WC, Xu YF. Consensus models for AHP group decision making under row geometric mean prioritization method. Decision Support Systems. 2010;49(3):281–289. doi:10.1016/j.dss.2010.03.003.
• [27] Srdjevic B. Combining different prioritization methods in AHP synthesis. Computers and Operations Research. 2005;32(7):1897–1919. doi:10.1016/j.cor.2003.12.005.
• [28] 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.
• [29] Aguaron J, Moreno-Jim´enez JM. The geometric consistency index: Approximated thresholds. European Journal of Operational Research. 2003;147(1):137–145. doi:10.1016/S0377-2217(02)00255-2.
• [30] Forman E, Peniwati K. Aggregating individual judgments and priorities with the analytic hierarchy process. European Journal of Operational Research. 1998;108:165–169. doi:10.1016/S0377-2217(97)00244-0.
• [31] Barzilai J, Golany B. AHP rank reversal normalization and aggregation rules. INFOR. 1994;32:57–64. Available from: http://hdl.handle.net/10222/43855.
• [32] Herrera-Viedma E, Herrera F, Chiclana F, Luque M. A consensus model for multiperson decision making with different preference structures. IEEE Systems, Man, and Cybernetics Society. 2002;32(3):394–402. ISSN:1083-4427. doi:10.1109/TSMCA.2002.802821.
• [33] Kacprzyk J, Fedrizzi M. A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research. 1988;34(3):316–325. doi:10.1016/0377-2217(88)90152-X.
• [34] Golany B, Kress M. A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices. European Journal of Operational Research. 1993;69(2):210–220. doi:10.1016/0377-2217(93)90165-J.
• [35] Kou G, Lin C. A cosine maximization method for the priority vector derivation in AHP. European Journal of Operational Research. 2014;235(1):225–232. doi:10.1016/j.ejor.2013.10.019.
• [36] Mikhailov L, Singh MG. Comparison analysis of methods for deriving priorities in the analytic hierarchy process. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. 1999;1:1037–1042. ISBN:0-7803-5731-0. doi:10.1109/ICSMC.1999.814236.
• [37] Mikhailov L, Knowles J. Priority elicitation in the AHP by a Pareto envelope-based selection algorithm. vol. 634 of Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg; 2010. ISBN:978-3-642-04045-0. doi:10.1007/978-3-642-04045-0 21.
• [38] Srdjevic B, Srdjevic Z. Bi-criteria evolution strategy in estimating weights from the AHP ratio-scale matrices. Applied Mathematics and Computation. 2011;218(4):1254–1266. doi:10.1016/j.amc.2011.06.006.
• [39] Srdjevic B, Srdjevic Z. Synthesis of individual best local priority vectors in AHP-group decision making. Applied Soft Computing. 2013;13(4):2045–2056. doi:10.1016/j.asoc.2012.11.010.
• [40] Yuen KKF. Analytic hierarchy prioritization process in the AHP application development: A prioritization operator selection approach. Applied Soft Computing. 2010;10(4):975–989. doi:10.1016/j.asoc.2009.08.041.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

Identyfikatory

DOI

10.3233/FI-2016-1342