Abstract
To express the uncertain preferred and non-preferred qualitative judgments of decision makers, interval-valued intuitionistic linguistic fuzzy sets (IVILFSs) are proposed in a similar way as Atanassov and Gargov’s interval-valued intuitionistic fuzzy sets. Considering the application of IVILFSs, the concept of interval-valued intuitionistic linguistic fuzzy variables (IVILFVs) is defined and a ranking order is offered. Then, we introduce interval-valued intuitionistic linguistic fuzzy preference relations (IVILFPRs) whose elements are IVILFVs. Furthermore, an additive consistency concept is presented and a model for judging the consistency of IVILFPRs is built. Meanwhile, optimization models for deriving additively consistent IVILFPRs and for determining missing linguistic variables in incomplete IVILFPRs are constructed, respectively. For group decision making, optimization models for determining the weights of the decision makers and for improving the consensus level are established, respectively. A procedure for group decision making with IVILFPRs is developed that can cope with inconsistent and incomplete IVILFPRs. Finally, a practical group decision-making problem about evaluating express companies is selected to show the application of the new results.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
Atanassov, K. T., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 343–349.
Beliakov, G., James, S., & Wilkin, T. (2017). Aggregation and consensus for preference relations based on fuzzy partial orders. Fuzzy Optimization and Decision Making, 16, 409–428.
Cabrerizo, F. J., Al-Hmouz, R., Morfeq, A., Balamash, A. S., Martínez, M. A., & Herrera-Viedma, E. (2017). Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Computing, 21, 3037–3050.
Chen, Z. C., Liu, P. H., & Pei, Z. (2015). An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. International Journal of Computational Intelligence Systems, 8, 747–760.
Goyal, R. K., & Kaushal, S. (2018). Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization. Fuzzy Optimization and Decision Making, 17, 195–209.
Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1996). A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 78, 73–87.
Liu, W., Dong, Y. C., Chiclana, F., Cabrerizo, F. J., & Herrera-Viedma, E. (2017). Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optimization and Decision Making, 16, 429–447.
Meng, F. Y., & Chen, X. H. (2018). A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations. Fuzzy Optimization and Decision Making, 17, 49–73.
Meng, F. Y., Tang, J., Wang, P., & Chen, X. H. (2018). A programming-based algorithm for interval-valued intuitionistic fuzzy group decision making. Knowledge-Based Systems, 144, 122–143.
Meng, F. Y., Tang, J., & Xu, Z. S. (2017a). A 0-1 mixed programming model based method for group decision making with intuitionistic fuzzy preference relations. Computers & Industrial Engineering, 112, 289–304.
Meng, F. Y., Tang, J., & Xu, Z. S. (2017b). Exploiting the priority weights from interval linguistic fuzzy preference relations. Soft Computing. https://doi.org/10.1007/s00500-017-2878-y.
Park, J. H., Gwak, M. G., & Kwun, Y. C. (2011). Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making. Computing, 93, 47–64.
Tang, J., Meng, F., & Zhang, Y. (2018). Decision making with interval-valued intuitionistic fuzzy preference relations based on additive consistency analysis. Information Sciences, 467, 115–134.
Tapia García, J. M., del Moral, M. J., Martinez, M. A., & Herrera-Viedma, E. (2012). A consensus model for group decision making problems with linguistic interval fuzzy preference relations. Expert Systems with Applications, 39, 10022–10030.
Xu, Z. S. (2004a). EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 791–810.
Xu, Z. S. (2004b). Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information Sciences, 168, 171–184.
Xu, Z. S. (2006). An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decision Support Systems, 41, 488–499.
Xu, Z. S. (2007a). Intuitionistic preference relations and their application in group decision making. Information Sciences, 177, 2363–2379.
Xu, Z. S. (2007b). A survey of preference relations. International Journal of General Systems, 36, 179–203.
Xu, Z. S. (2010). An integrated model-based interactive approach to FMAGDM with incomplete preference information. Fuzzy Optimization and Decision Making, 9, 333–357.
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning–Part I. Information Sciences, 8, 199–249.
Zeng, S. Z., Merigo, J. M., & Su, W. H. (2013). The uncertain probabilistic OWA distance operator and its application in group decision making. Mathematical and Computer Modelling, 37, 6266–6275.
Zhou, L. G., He, Y. D., Chen, H. Y., & Liu, J. P. (2014a). On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA. Applied Intelligence, 40, 229–243.
Zhou, L. G., Wu, J. X., & Chen, H. Y. (2014b). Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making. Appl. Soft Computing, 25, 266–276.
Acknowledgements
The work was supported by the Grant from the FEDER funds provided by the Spanish Ministry of Economy and Competitiveness (No. TIN2016-75850-R), the National Natural Science Foundation of China (Nos. 71571192, and 71671188), the Innovation-Driven Project of Central South University (No. 2018CX039), the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts094), the Major Project for National Natural Science Foundation of China (Nos. 91846301, 71790615), and the State Key Program of National Natural Science of China (No. 71431006).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tang, J., Meng, F., Cabrerizo, F.J. et al. A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations. Fuzzy Optim Decis Making 18, 493–527 (2019). https://doi.org/10.1007/s10700-019-09304-w
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10700-019-09304-w