Document Type : Research Paper



Increasing the complexity of decision-making problems leads to utilize a group of experts instead of one expert for evaluating the contractor selection problem. This paper proposes a hesitant fuzzy preference selection index method based on risk preferences of experts. The hesitant fuzzy set is used to cope with the uncertainty in vague/hesitant situations. Also, the compromise solution is proposed to compute the weight of each expert. Moreover, the proposed approach considers the quantitative and qualitative criteria and also assists the experts to reduce margin of errors by assigning some membership degrees for each contractor versus each criterion under a set. In addition, the experts' judgments are aggregated in the last step of proposed approach in the group decision process to avoid the data loss. In the presented approach, selecting the best contractor is based on closest to positive ideal and farthest from negative ideal, simultaneously. Finally, the proposed method is applied to a case in construction industry for selecting the suitable contractor, in which the obtained results are compared with two decision methods from the recent literature to indicate the efficiency and validity of the proposed method.


Alonso, S., et al., A consistency‐based procedure to estimate missing pairwise preference values. International Journal of Intelligent Systems, 2008. 23(2): p. 155-175.
Alonso, S., et al., A web based consensus support system for group decision making problems and incomplete preferences. Information Sciences, 2010. 180(23): p. 4477-4495.
Büyüközkan, G. and G. Çifçi, A new incomplete preference relations based approach to quality function deployment. Information Sciences, 2012. 206: p. 30-41.
Chang, C.-L., A modified VIKOR method for multiple criteria analysis. Environmental monitoring and assessment, 2010. 168(1-4): p. 339-344.
Chen, C.-T., Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets and Systems, 2000. 114(1): p. 1-9.
Chen, C.-T., C.-T. Lin, and S.-F. Huang, A fuzzy approach for supplier evaluation and selection in supply chain management. International journal of production economics, 2006. 102(2): p. 289-301.
Chen, S.-M. and S.-J. Niou, Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Systems with Applications, 2011. 38(4): p. 3865-3872.
Chiclana, F., et al., Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. Fuzzy Systems, IEEE Transactions on, 2009. 17(1): p. 14-23.
Ebrahimnejad, S., et al., A novel two-phase group decision making approach for construction project selection in a fuzzy environment. Applied Mathematical Modelling, 2012. 36(9): p. 4197-4217.
Fu, C. and S.-L. Yang, The group consensus based evidential reasoning approach for multiple attributive group decision analysis. European Journal of Operational Research, 2010. 206(3): p. 601-608.
Fu, C. and S. Yang, An attribute weight based feedback model for multiple attributive group decision analysis problems with group

consensus requirements in evidential reasoning context. European Journal of Operational Research, 2011. 212(1): p. 179-189.
Genç, S., et al., Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations. Information Sciences, 2010. 180(24): p. 4877-4891.
Herrera-Viedma, E., F. Herrera, and F. Chiclana, A consensus model for multiperson decision making with different preference structures. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 2002. 32(3): p. 394-402.
Herrera-Viedma, E., et al., A consensus support system model for group decision-making problems with multigranular linguistic preference relations. Fuzzy Systems, IEEE Transactions on, 2005. 13(5): p. 644-658. Junior FR, Osiro L, Carpinetti LC, A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection. Applied Soft Computing, 2014. 31(21): p. 194-209.
Kacprzyk, J., M. Fedrizzi, and H. Nurmi, Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems, 1992. 49(1): p. 21-31. Kannan, Devika, Ana Beatriz Lopes de Sousa Jabbour, and Charbel José Chiappetta Jabbour, Selecting green suppliers based on GSCM practices: Using fuzzy TOPSIS applied to a Brazilian electronics company. European Journal of Operational Research, 2014. 233(2): p. 432-447.
Liao, H. and Z. Xu, Subtraction and division operations over hesitant fuzzy sets. Journal of Intelligent and Fuzzy Systems, 2013.
Liao, H. and Z. Xu, A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optimization and Decision Making, 2013. 12(4): p. 373-392.
Maniya, K. and M. Bhatt, A selection of material using a novel type decision-making method: preference selection index method. Materials & Design, 2010. 31(4): p. 1785-1789.

Mata, F., L. Martínez, and E. Herrera-Viedma, An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context. Fuzzy Systems, IEEE Transactions on, 2009. 17(2): p. 279-290. Nazam M, Xu J, Tao Z, Ahmad J, Hashim M, A fuzzy AHP-TOPSIS framework for the risk assessment of green supply chain implementation in the textile industry. International Journal of Supply and Operations Management, 2015, 2(1): p. 548-68.
Pérez, I.J., F.J. Cabrerizo, and E. Herrera-Viedma, A mobile decision support system for dynamic group decision-making problems. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 2010. 40(6): p. 1244-1256.
Tanino, T., Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 1984. 12(2): p. 117-131.
Torra, V., Hesitant fuzzy sets. International Journal of Intelligent Systems, 2010. 25(6): p. 529-539.
Torra, V. and Y. Narukawa. On hesitant fuzzy sets and decision. in Fuzzy Systems, 2009. FUZZ-IEEE 2009. IEEE International Conference on. 2009: IEEE. Vahdani, B., et al. A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment. Applied Mathematical Modeling, 2013. 37(4): p. 1781-1799.
Vahdani, B., et al., A new compromise solution method for fuzzy group decision-making problems with an application to the contractor selection. Engineering Applications of Artificial Intelligence, 2013. 26(2): p. 779-788.
Vahdani, B., S.M. Mousavi, and R. Tavakkoli-Moghaddam, Group decision making based on novel fuzzy modified TOPSIS method. Applied Mathematical Modelling, 2011. 35(9): p. 4257-4269.
Wang, T.-C. and Y.-H. Chen, Incomplete fuzzy linguistic preference relations under uncertain environments. Information Fusion, 2010. 11(2): p. 201-207.

Wei, G., Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowledge-Based Systems, 2012. 31: p. 176-182.
Xia, M. and Z. Xu, Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 2011. 52(3): p. 395-407.
Xu, Z., Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. International journal of approximate reasoning, 2004. 36(3): p. 261-270.
Xu, Z., A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 2004. 166(1): p. 19-30.
Xu, Z., Multiple-attribute group decision making with different formats of preference information on attributes. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 2007. 37(6): p. 1500-1511.
Xu, Z., Group decision making based on multiple types of linguistic preference relations. Information Sciences, 2008. 178(2): p. 452-467.
Xu, Z. and X. Zhang, Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 2013. 52: p. 53-64.
Zhang, N. and G. Wei, Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Applied Mathematical Modelling, 2013. 37(7): p. 4938-4947.
Zhang, Z., et al., Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Computers & Industrial Engineering, 2014. 67: p. 116-138.
Zhu, B., Z. Xu, and M. Xia, Hesitant fuzzy geometric Bonferroni means. Information Sciences, 2012. 205: p. 72-85