166
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

New additive consistency framework and utility derivation for interval fuzzy reciprocal preference relations

, , &
Pages 2572-2590 | Received 24 May 2021, Accepted 05 Nov 2021, Published online: 15 Dec 2021

References

  • Al Salem, A. A., & Awasthi, A. (2018). Investigating rank reversal in reciprocal fuzzy preference relation based on additive consistency: Causes and solutions. Computers & Industrial Engineering, 115, 573–581. https://doi.org/10.1016/j.cie.2017.11.027
  • Barrenechea, E., Fernandez, J., Pagola, M., Chiclana, F., & Bustince, H. (2014). Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making. Knowledge-Based Systems, 58, 33–44. https://doi.org/10.1016/j.knosys.2013.10.002
  • Bentkowska, U., Bustince, H., Jurio, A., Pagola, M., & Pekala, B. (2015). Decision making with an interval-valued fuzzy preference relation and admissible orders. Applied Soft Computing, 35, 792–801. https://doi.org/10.1016/j.asoc.2015.03.012
  • Brunelli, M., & Fedrizzi, M. (2015). Axiomatic properties of inconsistency indices for pairwise comparisons. Journal of the Operational Research Society, 66(1), 1–15. https://doi.org/10.1057/jors.2013.135
  • Cavallo, B. (2017). Computing random consistency indices and assessing priority vectors reliability. Information Sciences, 420, 532–542. https://doi.org/10.1016/j.ins.2017.08.082
  • Cavallo, B., & Brunelli, M. (2018). A general unified framework for interval pairwise comparison matrices. International Journal of Approximate Reasoning, 93, 178–198. https://doi.org/10.1016/j.ijar.2017.11.002
  • Cavallo, B., Ishizaka, A., Olivieri, M. G., & Squillante, M. (2019). Comparing inconsistency of pairwise comparison matrices depending on entries. Journal of the Operational Research Society, 70(5), 842–850. https://doi.org/10.1080/01605682.2018.1464427
  • Crawford, G., & Williams, C. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29(4), 387–405. https://doi.org/10.1016/0022-2496(85)90002-1
  • Duleba, S. (2020). Introduction and comparative analysis of the multi-level parsimonious AHP methodology in a public transport development decision problem. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2020.1824553
  • Duleba, S., & Blahota, I. (2021). Determining optimal group weights for consensus creation in AHP for three conflicting stakeholder groups by vector distance minimization. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2021.1918588
  • Fedrizzi, M., & Brunelli, M. (2009). On the normalisation of a priority vector associated with a reciprocal relation. International Journal of General Systems, 38(5), 579–586. https://doi.org/10.1080/03081070902753606
  • Fedrizzi, M., & Brunelli, M. (2010). On the priority vector associated with a reciprocal relation and a pairwise comparison matrix. Soft Computing, 14(6), 639–645. https://doi.org/10.1007/s00500-009-0432-2
  • Fedrizzi, M., & Krejčí, J. (2015). A note on the paper fuzzy analytic hierarchy process: Fallacy of the popular methods. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 23(06), 965–970. https://doi.org/10.1142/S0218488515500440
  • Fu, C., Chang, W., Liu, W., & Yang, S. (2021). Consistency of distributed preference relations. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2020.1865849
  • Gong, Z., Tan, X., & Yang, Y. (2019). Optimal weighting models based on linear uncertain constraints in intuitionistic fuzzy preference relations. Journal of the Operational Research Society, 70(8), 1296–1307. https://doi.org/10.1080/01605682.2018.1489349
  • Guo, W., Gong, Z., Xu, X., & Herrera-Viedma, E. (2021). Additive and multiplicative consistency modeling for incomplete linear uncertain preference relations and its weight acquisition. IEEE Transactions on Fuzzy Systems, 29(4), 805–819. https://doi.org/10.1109/TFUZZ.2020.2965909
  • He, Y., & Xu, Z. (2018). A consensus framework with different preference ordering structures and its applications in human resource selection. Computers & Industrial Engineering, 118, 80–88. https://doi.org/10.1016/j.cie.2018.02.022
  • Herrera-Viedma, E., Herrera, F., Chiclana, F., & Luque, M. (2004). Some issues on consistency of fuzzy preference relations. European Journal of Operational Research, 154(1), 98–109. https://doi.org/10.1016/S0377-2217(02)00725-7
  • Ishizaka, A., & Siraj, S. (2018). Are multi-criteria decision-making tools useful? An experimental comparative study of three methods. European Journal of Operational Research, 264(2), 462–471. https://doi.org/10.1016/j.ejor.2017.05.041
  • Khorshidi, H. A., & Aickelin, U. (2020). Multicriteria group decision-making under uncertainty using interval data and cloud models. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2020.1796541
  • Krejčí, J. (2017a). On additive consistency of interval fuzzy preference relations. Computers & Industrial Engineering, 107, 128–140. https://doi.org/10.1016/j.cie.2017.03.002
  • Krejčí, J. (2017b). On multiplicative consistency of interval and fuzzy reciprocal preference relations. Computers & Industrial Engineering, 111, 67–78. https://doi.org/10.1016/j.cie.2017.07.002
  • Krejčí, J. (2019). On extension of multiplicative consistency to interval fuzzy preference relations. Operational Research, 19(3), 783–815. https://doi.org/10.1007/s12351-017-0307-8
  • Kułakowski, K., Mazurek, J., & Strada, M. (2021). On the similarity between ranking vectors in the pairwise comparison method. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2021.1947754
  • Li, C.-C., Dong, Y., Xu, Y., Chiclana, F., Herrera-Viedma, E., & Herrera, F. (2019). An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and fusion: Taxonomy and future directions. Information Fusion, 52, 143–156. https://doi.org/10.1016/j.inffus.2018.12.004
  • Liu, F., Peng, Y. N., Yu, Q., & Zhao, H. (2018). A decision-making model based on interval additive reciprocal matrices with additive approximation-consistency. Information Sciences, 422, 161–176. https://doi.org/10.1016/j.ins.2017.09.014
  • Liu, F., Zhang, W. G., & Fu, J. H. (2012). A new method of obtaining the priority weights from an interval fuzzy preference relation. Information Sciences, 185(1), 32–42. https://doi.org/10.1016/j.ins.2011.09.019
  • Liu, F., Zhang, J. W., Yu, Q., Peng, Y. N., & Pedrycz, W. (2020). On weak consistency of interval additive reciprocal matrices. Fuzzy Optimization and Decision Making, 19(2), 153–175. https://doi.org/10.1007/s10700-020-09314-z
  • Li, B., Zhang, Y., & Xu, Z. (2021). Limited interval-valued probabilistic linguistic term sets in evaluating airline service quality. Journal of the Operational Research Society, 72(6), 1330–1346. https://doi.org/10.1080/01605682.2020.1718014
  • Meng, F., & Tang, J. (2020). A comparative study for consistency-based decision making with interval multiplicative preference relations. International Journal of General Systems, 49(4), 400–437. https://doi.org/10.1080/03081079.2020.1729759
  • Meng, F., Tang, J., & Fujita, H. (2019). Consistency-based algorithms for decision-making with interval fuzzy preference relations. IEEE Transactions on Fuzzy Systems, 27(10), 2052–2066. https://doi.org/10.1109/TFUZZ.2019.2893307
  • Mi, X., Liao, H., & Zeng, X. J. (2021). Transitivity and approximate consistency threshold determination for reciprocal preference relations in group decision making. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2021.1928560
  • Orlovski, S. A. (1978). Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, 1, 155–167.
  • Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill.
  • Saaty, T. L., & Vargas, L. G. (1987). Uncertainty and rank order in the analytic hierarchy process. European Journal of Operational Research, 32(1), 107–117. https://doi.org/10.1016/0377-2217(87)90275-X
  • Song, Y., Li, G., Ergu, D., & Liu, N. (2021). An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations. Journal of the Operational Research Society, https://doi.org/10.1080/01605682.2021.1873079
  • Tang, M., Liao, H., Mi, X., Xu, X., & Herrera, F. (2021). Dynamic subgroup-quality-based consensus in managing consistency, nearness, and evenness quality indices for large-scale group decision making under hesitant environment. Journal of the Operational Research Society, 72(4), 865–878. https://doi.org/10.1080/01605682.2019.1708823
  • Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 12(2), 117–131. https://doi.org/10.1016/0165-0114(84)90032-0
  • Wajch, E. (2019). From pairwise comparisons to consistency with respect to a group operation and Koczkodaj’s metric. International Journal of Approximate Reasoning, 106, 51–62. https://doi.org/10.1016/j.ijar.2018.12.016
  • Wan, S., Wang, F., & Dong, J. (2018). A group decision making method with interval valued fuzzy preference relations based on the geometric consistency. Information Fusion, 40, 87–100. https://doi.org/10.1016/j.inffus.2017.06.003
  • Wang, Z. J. (2014). A note on “Incomplete interval fuzzy preference relations and their applications. Computers & Industrial Engineering, 77, 65–69. https://doi.org/10.1016/j.cie.2014.09.011
  • Wang, Z. J., & Li, K. W. (2012). Goal programming approaches to deriving interval weights based on interval fuzzy preference relations. Information Sciences, 193, 180–198. https://doi.org/10.1016/j.ins.2012.01.019
  • Wang, Z. J., Lin, J., & Liu, F. (2019). Axiomatic property based consistency analysis and decision making with interval multiplicative reciprocal preference relations. Information Sciences, 491, 109–137. https://doi.org/10.1016/j.ins.2019.04.002
  • Wang, Z. J., & Wu, Y. K. (2021). Minimum adjustment cost-based multi-stage goal programming models for consistency improving and consensus building with multiplicative reciprocal paired comparison matrices. Journal of the Operational Research Society, 2021.1935336. https://doi.org/10.1080/01605682
  • Wang, Z. J., Yang, X., & Jin, X. T. (2020). And-like-uninorm-based transitivity and analytic hierarchy process with interval-valued fuzzy preference relations. Information Sciences, 539, 375–396. https://doi.org/10.1016/j.ins.2020.05.052
  • Wu, J., & Chiclana, F. (2014a). A social network analysis trust-consensus based approach to group decision making problems with interval-valued fuzzy reciprocal preference relations. Knowledge-Based Systems, 59, 97–107. https://doi.org/10.1016/j.knosys.2014.01.017
  • Wu, J., & Chiclana, F. (2014b). Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowledge-Based Systems, 71, 187–200. https://doi.org/10.1016/j.knosys.2014.07.024
  • Wu, J., Chiclana, F., & Liao, H. (2018). Isomorphic multiplicative transitivity for intuitionistic and interval-valued fuzzy preference relations and its application in deriving their priority vectors. IEEE Transactions on Fuzzy Systems, 26(1), 193–202. https://doi.org/10.1109/TFUZZ.2016.2646749
  • Wu, Z., Yang, X., Tu, J., & Chen, X. (2020). Optimal consistency and consensus models for interval additive preference relations: A discrete distribution perspective. Journal of the Operational Research Society, 71(9), 1479–1497. https://doi.org/10.1080/01605682.2019.1621219
  • Xia, M., & Xu, Z. (2011). Some issues on multiplicative consistency of interval reciprocal relations. International Journal of Information Technology & Decision Making, 10(06), 1043–1065. https://doi.org/10.1142/S0219622011004701
  • Xia, M., & Xu, Z. (2014). Interval weight generation approaches for reciprocal relations. Applied Mathematical Modelling, 38(3), 828–838. https://doi.org/10.1016/j.apm.2013.07.018
  • Xu, Z. (2007). A survey of fuzzy preference relations. International Journal of General Systems, 36(2), 179–203. https://doi.org/10.1080/03081070600913726
  • Xu, Z., & Chen, J. (2008). Some models for deriving the priority weights from interval fuzzy preference relations. European Journal of Operational Research, 184(1), 266–280. https://doi.org/10.1016/j.ejor.2006.11.011
  • Xu, Y., Li, K. W., & Wang, H. (2014). Incomplete interval fuzzy preference relations and their applications. Computers & Industrial Engineering, 67, 93–103. https://doi.org/10.1016/j.cie.2013.10.010
  • Yang, W., Jhang, S., Shi, S., Xu, Z., & Ma, Z. (2020). A novel additive consistency for intuitionistic fuzzy preference relations in group decision making. Applied Intelligence, 50(12), 4342–4356. https://doi.org/10.1007/s10489-020-01796-z
  • Zhang, H. (2019). Revisiting multiplicative consistency of interval fuzzy preference relation. Computers & Industrial Engineering, 132, 325–332. https://doi.org/10.1016/j.cie.2019.04.030
  • Zhang, Z., Kou, X., Yu, W., & Gao, Y. (2021). Consistency improvement for fuzzy preference relations with self-confidence: An application in two-sided matching decision making. Journal of the Operational Research Society, 72(8), 1914–1927. https://doi.org/10.1080/01605682.2020.1748529
  • Zhang, C., Liao, H., & Luo, L. (2019). Additive consistency-based priority-generating method of q-rung orthopair fuzzy preference relation. International Journal of Intelligent Systems, 34(9), 2151–2176. https://doi.org/10.1002/int.22137

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.