Fuzzy Optimization and Decision Making

, Volume 18, Issue 4, pp 493–527 | Cite as

A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations

  • Jie Tang
  • Fanyong MengEmail author
  • Francisco Javier Cabrerizo
  • Enrique Herrera-ViedmaEmail author


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.


Decision making IVILFPR Consistency Consensus Optimization model 



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).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaChina
  2. 2.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain
  3. 3.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.School of Management Science and EngineeringNanjing University of Information Science and TechnologyNanjingChina

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