A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making
In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.
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Volume (Year): 218 (2012)
Issue (Month): 3 ()
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- Lin, Robert & Lin, Jennifer Shu-Jen & Chang, Jason & Tang, Didos & Chao, Henry & Julian, Peter C, 2008. "Note on group consistency in analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 190(3), pages 672-678, November.
- Fedrizzi, Michele & Giove, Silvio, 2007.
"Incomplete pairwise comparison and consistency optimization,"
European Journal of Operational Research,
Elsevier, vol. 183(1), pages 303-313, November.
- Michele Fedrizzi & Silvio Giove, 2006. "Incomplete pairwise comparison and consistency optimization," Working Papers 144, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
- Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
- S. Alonso & E. Herrera-Viedma & F. Chiclana & F. Herrera, 2009. "Individual And Social Strategies To Deal With Ignorance Situations In Multi-Person Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 313-333.
- Siraj, Sajid & Mikhailov, Ludmil & Keane, John, 2012. "A heuristic method to rectify intransitive judgments in pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 420-428.
- Islam, R. & Biswal, M. P. & Alam, S. S., 1997. "Preference programming and inconsistent interval judgments," European Journal of Operational Research, Elsevier, vol. 97(1), pages 53-62, February.
- Wang, Ying-Ming & Elhag, Taha M.S., 2007. "A goal programming method for obtaining interval weights from an interval comparison matrix," European Journal of Operational Research, Elsevier, vol. 177(1), pages 458-471, February.
- Xu, Z., 2000. "On consistency of the weighted geometric mean complex judgement matrix in AHP," European Journal of Operational Research, Elsevier, vol. 126(3), pages 683-687, November.
- Podinovski, Vladislav V., 2007. "Interval articulation of superiority and precise elicitation of priorities," European Journal of Operational Research, Elsevier, vol. 180(1), pages 406-417, July.
- Arbel, Ami, 1989. "Approximate articulation of preference and priority derivation," European Journal of Operational Research, Elsevier, vol. 43(3), pages 317-326, December.
- Herrera, F. & Martinez, L. & Sanchez, P. J., 2005. "Managing non-homogeneous information in group decision making," European Journal of Operational Research, Elsevier, vol. 166(1), pages 115-132, October.
- Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
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