Abstract
We propose the new compatibility of interval multiplicative preference relations (IMPRs) in the group decision making (GDM) and apply it to determine the weights of experts. Firstly, we introduce the operation of interval numbers and define the new conception of logarithm compatibility degree of two interval multiplicative preference relations. Then, we prove the properties of logarithm compatibility of IMPR. It is pointed that if IMPR provided by every expert and its characteristic matrix are of acceptable compatibility, then the synthetic preference relation and the synthetic characteristic matrix are also of acceptable compatibility. Furthermore, we construct a mathematical programming model to determine the optimal weights of experts by minimizing the square logarithm compatibility in the GDM with IMPR and discuss the solution to the model. Finally, a numerical example is illustrated to show that the model is feasible.
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References
Arbel A (1989) Approximate articulation of preference and priority derivation. Eur J Oper Res 43: 317–326
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96
Chen HY, Zhou LG, Han B (2011) On compatibility of uncertain additive linguistic preference relations and its application in the group decision making. Knowl Based Syst 24: 816–823
Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst 97: 33–48
Fedrizzi M, Brunelli M (2009) On the normalisation of a priority vector associated with a reciprocal relation. Int J Gen Syst 38: 579–586
Haines LM (1998) A statistical approach to the analytic hierarchy process with interval judgments. Eur J Oper Res 110: 112–125
Islam R, Biswal MP, Alam SS (1997) Preference programming and inconsistent interval judgments. Eur J Oper Res 97: 53–62
Kacprzyk J (1986) Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst 18: 105–118
Kacprzyk J, Fedrizzi M, Nurmi H (1992) Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst 49: 21–31
Mikhailov L (2002) Fuzzy analytical approach to partnership selection in formation of virtual enterprises. Omega 30: 393–401
Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York
Saaty TL (1994) A ratio scale metric and the compatibility of ratio scales: the possibility of Arrow’s impossibility theorem. Appl Math Lett 7: 51–57
Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32: 107–117
Saaty TL, Vargas LG (2007) Dispersion of group judgments. Math Comput Model 46: 918–925
Salo A, Hämäläinen RP (1995) Preference programming through approximate ratio comparisons. Eur J Oper Res 82: 458–475
Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12: 117–131
Wang YM, Yang JB, Xu DL (2005) A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst 152: 475–498
Xu ZS (2004) On compatibility of interval fuzzy preference relations. Fuzzy Optim Decis Mak 3: 217–225
Xu ZS (2007) A survey of preference relations. Int J Gen Syst 36: 179–203
Xu ZS (2011) Consistency of interval fuzzy preference relations in group decision making. Appl Soft Comput 11: 3898–3909
Xu ZS, Da QL (2005) A least deviation method to obtain a priority vector of a fuzzy preference relation. Eur J Oper Res 164: 206–216
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Wang, Y., Chen, H. & Zhou, L. Logarithm Compatibility of Interval Multiplicative Preference Relations with an Application to Determining the Optimal Weights of Experts in the Group Decision Making. Group Decis Negot 22, 759–772 (2013). https://doi.org/10.1007/s10726-012-9291-9
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DOI: https://doi.org/10.1007/s10726-012-9291-9