References
- R. M. Rodríguez, L. Martínez and F. Herrera, “A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets,” Inf. Sci., 241, 28–42 (2013).
- T. L. Saaty, “A scaling method for priorities in hierarchical structures,” J. Math. Psychol., 15, 234–281 (1977).
- S. A. Orlovsky, “Decision-making with a fuzzy preference relation,” Fuzzy Set Syst., 1, 155–167 (1978).
- F. Herrera, E. Herrera-Viedma and J. L. Verdegay, “A model of consensus in group decision making under linguistic assessments,” Fuzzy Set Syst., 78, 73–87 (1996).
- F. Chiclana, E. Herrera-Viedma, F. Herrera and S. Alonso, “Some induced ordered weighted averaging operators and their use for solving group decisionmaking problems based on fuzzy preference relations,” Eur. J. Oper. Res., 182, 383–399 (2007).
- Y. Dong, Y. Xu and S. Yu, “Linguistic multiperson decision making based on the use of multiple preference relations,” Fuzzy Set Syst., 160, 603–623 (2009).
- Y. Dong, G. Zhang, W. Hong and Y. Xu, “Consensus models for AHP group decision making under row geometric mean prioritization method,” Decis. Support Syst., 49, 281–289 (2010).
- Z. Zhang and C. Guo, “Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations,” Int. J. Syst. Sci., doi: 10.1080/00207721.2014.999732 (2016).
- F. Chiclana, E. Herrera-Viedma, S. Alonso and F. Herrera, “Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity,”jIEEE Trans. Fuzzy Syst., 17, 14–23 (2009).
- E. Herrera-Viedma, F. J. Cabrerizo, J. Kacprzyk and W. Pedrycz, “A review of soft consensus models in a fuzzy environment,” Inf. Fusion, 17, 4–13 (2014).
- E. Herrera-Viedma, F. Herrera, F. Chiclana and M. Luque, “Some issues on consistency of fuzzy preference relations,” Eur. J. Oper. Res., 154, 98–109 (2004).
- J. Ma, Z. Fan, Y. Jiang, J. Mao and L. Ma, “A method for repairing the inconsistency of fuzzy preference relations,”jFuzzy Set Syst., 157, 20–33 (2006).
- E. Herrera-Viedma, S. Alonso, F. Chiclana and F. Herrera, “A consensus model for group decision making with incomplete fuzzy preference relations,” IEEE Trans. Fuzzy Syst., 15, 863–877 (2007).
- T. Tanino, “Fuzzy preference orderings in group decision making,” Fuzzy Set Syst., 12, 117–131 (1984).
- Z. Wu and J. Xu, “A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures,” Fuzzy Set Syst., 206, 58–73 (2012).
- M. Xia, Z. Xu and J. Chen, “Algorithms for improving consistency or consensus of reciprocal [0,1]-valued preference relations,” Fuzzy Set Syst., 216, 108–133 (2013).
- Z. S. Xu, “Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation,” Int. J. Approx. Reasoning, 36, 261–270 (2004).
- M. Fedrizzi and S. Giove, “Incomplete pairwise comparison and consistency optimization,” Eur. J. Oper. Res., 183, 303–313 (2007).
- F. J. Cabrerizo, R. Heradio, I. J. P´erez and E. Herrera-Viedma, “A selection process based on additive consistency to deal with incomplete fuzzy linguistic information,” J. Univers. Comput. Sci., 16, 62–81 (2010).
- E. Herrera-Viedma, F. Chiclana, F. Herrera and S. Alonso, “Group decision-making model with incomplete fuzzy preference relations based on additive consistency,” IEEE Trans. Syst. Man Cybern. Part BCybern., 37, 176–189 (2007).
- Z. Zhang and C. Guo, “Consistency-based algorithms to estimate missing elements for uncertain 2-tuple linguistic preference relations,” Int. J. Comput. Intell. Syst., 7, 924–936 (2014).
- R. Ure˜na, F. Chiclana, J. A. Morente and E. Herrera-Viedma, “Managing incomplete preference relations in decision making: A review and future trends,” Inf. Sci., 302, 14–32 (2015).
- S. Alonso, F. Chiclana, F. Herrera, E. Herrera-Viedma, J. Alcal´a-Fdez and C. Porcel, “A consistency-based procedure to estimate missing pairwise preference values,” Int. J. Intell. Syst., 23, 155–175 (2008).
- F. Chiclana, E. Herrera-Viedma, S. Alonso and F. Herrera, “A note on the estimation of missing pairwise preference values: a uninorm consistency based method,” Int. J. Uncertainty Fuzziness Knowl.-Based Syst., 16, 19–32 (2008).
- Z. Gong, “Least-square method to priority of the fuzzy preference relations with incomplete information,” Int. J. Approx. Reason., 47, 258–264 (2008).
- X. Liu, Y. Pan, Y. Xu and S. Yu, “Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations,” Fuzzy Set Syst., 198, 1–19 (2012).
- Y. Jiang and Z. Fan, “An approach to group decision making based on incomplete fuzzy preference relations,” Int. J. Uncertainty Fuzziness Knowl.-Based Syst., 16, 83–94 (2008).
- Z. Zhang and C. Guo, “Notes on ‘Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations’,” Appl. Math. Model., 40, 1788–1792 (2016).
- K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Set Syst., 20, 87–96 (1986).
- D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York: Academic Press (1980).
- I. T. Turksen, “Interval valued fuzzy sets based on normal forms,” Fuzzy Set Syst., 20, 191–210 (1986).
- R. R. Yager, “On the theory of bags,” Int. J. Gen. Syst., 13, 23–37 (1986).
- R. M. Rodríguez, L. Martínez, V. Torra, Z. S. Xu and F. Herrera, “Hesitant fuzzy sets: state of the art and future directions,” Int. J. Intell. Syst., 29, 495–524 (2014).
- R. M. Rodríguez, B. Bedregal, H. Bustince, Y. C. Dong, B. Farhadinia, C. Kahraman, L. Martínez, V. Torra, Y. J. Xu, Z. S. Xu and F. Herrera, “A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress,” Inf. Fusion, 29, 89–97 (2016).
- V. Torra, Y. Narukawa, “On hesitant fuzzy sets and decision,” in Proc. of the 18th IEEE Int. Conf. Fuzzy Syst., Jeju Island, Korea, 1378–1382 (2009).
- V. Torra, “Hesitant fuzzy sets,” Int. J. Intell. Syst., 25, 529–539 (2010).
- M. Xia and Z. Xu, “Hesitant fuzzy information aggregation in decision making,” Int. J. Approx. Reason., 52, 395–407 (2011).
- Z. Xu and M. Xia, “Distance and similarity measures for hesitant fuzzy sets,” Inf. Sci., 181, 2128–2138 (2011).
- H. Liao, Z. Xu and X. Zeng, “Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making,” Inf. Sci., 271, 125–142 (2014).
- X. Zhang and Z. Xu, “The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment,” Knowledge-Based Syst., 61, 48–58 (2014).
- B. Zhu and Z. Xu, “Regression methods for hesitant fuzzy preference relations,” Technol. Econ. Dev. Eco., 19, S214–S227 (2013).
- H. Liao, Z. Xu and M. Xia, “Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making,” Int. J. Inf. Technol. Decis. Mak. , 13, 47–76 (2014).
- R. M. Rodríguez, L. Martínez and F. Herrera, “Hesitant fuzzy linguistic term sets for decision making,” IEEE Trans. Fuzzy Syst., 20, 109–119 (2012).
- B. Zhu and Z. Xu, “Consistency measures for hesitant fuzzy linguistic preference relations,” IEEE Trans. Fuzzy Syst., 22, 35–45 (2014).
- N. Chen, Z. Xu and M. Xia, “Interval-valued hesitant preference relations and their applications to group decision making,” Knowledge-Based Syst., 37, 528–540 (2013).
- B. Zhu, Z. Xu and J. Xu, “Deriving a ranking from hesitant fuzzy preference relations under group decision making,” IEEE Trans. Cybern., 44, 1328–1337 (2014).
- M. Xia and Z. Xu, “Managing hesitant information in GDM problems under fuzzy and multiplicative preference relations,” Int. J. Uncertainty Fuzziness Knowl.-Based Syst., 21, 865–897 (2013).
- Z. Zhang and C. Wu, “A decision support model for group decision making with hesitant multiplicative preference relations,” Inf. Sci., 282, 136–166 (2014).
- B. Zhu and Z. Xu, “Analytic hierarchy processhesitant group decision making,” Eur. J. Oper. Res., 239, 794–801 (2014).
- G. Crawford and C. Williams, “A note on the analysis of subjective judgment matrices,” J. Math. Psychol., 29, 387–405 (1985).
- Y. Wang and Z. Fan, “Group decision analysis based on fuzzy preference relations: Logarithmic and geometric least squares methods,” Appl. Math. Comput., 194, 108–119 (2007).
- Y. Xu, R. Patnayakuni and H. Wang, “Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations,” Appl. Math. Model., 37, 2139–2152 (2013).
- Z. S. Xu. “Study on the relation between two classes of scales in AHP,” Syst. Eng. Theory Pract., 19, 97–101 (1999).
- Z. S. Xu, Uncertain Multiple Attribute Decision Making: Methods and Applications, Beijing: Tsinghua Univ. Press, Beijing (2004).
- Z. Xu, “Incomplete linguistic preference relations and their fusion,” Inf. Fusion, 7, 331–337 (2006).
- F. Herrera, L. Martínez and P. J. S´anchez, “Managing non-homogeneous information in group decision making,” Eur. J. Oper. Res., 166, 115–132 (2005).
- I. Palomares, R. M. Rodríguez and L. Martínez, “An attitude-driven web consensus support system for heterogeneous group decision making,” Expert Syst. Appl., 40, 139–149 (2013).
- Z. Zhang and C. Guo, “An approach to group decision making with heterogeneous incomplete uncertain preference relations,” Comput. Ind. Eng., 71, 27–36 (2014).
- X. Chen, H. Zhang and Y. Dong, “The fusion process with heterogeneous preference structures in group decision making: A survey,” Inf. Fusion, 24, 72–83 (2015).
- M. Xia and Z. Xu, “On consensus in group decision making based on fuzzy preference relations,” in E. Herrera-Viedma, et al. (Eds.), Consensual Processes, Berlin/Heidelberg: Springer, 263–287 (2011).
- Z. S. Xu and Q. L. Da, “Three reciprocal judgement matrices-based methods for priorities of complementary judgement matrices,” J. Southeast Univ. (Natural Science), 31, 106–107 (2001).
- T. L. Saaty, The Analytic Hierarchy Process, New York: McGraw-Hill (1980).
- S. Alonso, E. Herrera-Viedma, F. Chiclana and F. Herrera, Individual and social strategies to deal with ignorance situations in multi-person decision making,” Int. J. Inf. Technol. Decis. Mak., 8, 313–333 (2009).
- T. Chen, H. Wang and Y. Lu, “A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: A comparative perspective,” Expert Syst. Appl., 38, 7647–7658 (2011).
- H. Liu, J. Cai and L. Jiang, “On improving the additive consistency of the fuzzy preference relations based on comparative linguistic expressions,” Int. J. Intell. Syst., 29, 544–559 (2014).