Group Decision Making with Interval-Valued Intuitionistic Multiplicative Linguistic Preference Relations

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


To express the asymmetrically uncertain preferred and non-preferred qualitative judgments of decision makers, this paper introduces interval-valued intuitionistic multiplicative linguistic variables (IVIMLVs). To show their application in decision making, a ranking method is first offered. Then, we introduce IVIMLVs for preference relations and propose interval-valued intuitionistic multiplicative linguistic preference relations (IVIMLPRs). To obtain the ranking reasonably, a consistency definition for IVIMLPRs is presented. A mathematical optimization model for judging the consistency of IVIMLPRs based on the new concept is constructed. To address two general cases: incompleteness and inconsistency, mathematical optimization models for ascertaining unknown values in incomplete IVIMLPRs and deriving completely consistent IVIMLPRs from inconsistent ones are built, respectively. For group decision making, a consensus index is defined to measure the consensus achieved among the decision makers’ preferences. If the consensus is not enough, a mathematical optimization model for improving the consensus level is established. Furthermore, a linear optimization model for determining the weights of the decision makers based on the consensus analysis is constructed. Finally, a group decision-making method with IVIMLPRs based on consistency and consensus analysis is offered, and its application on selecting supply chain cooperative partners is offered.


Group decision making IVIMLPR Consistency Consensus Mathematical 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 (No. 71571192), the Beijing Intelligent Logistics System Collaborative Innovation Center (No. 2019KF-09), and the Innovation-Driven Project of Central South University (No. 2018CX039).


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Jie Tang
    • 1
  • Fanyong Meng
    • 1
    • 2
    Email author
  • Francisco Javier Cabrerizo
    • 3
  • Enrique Herrera-Viedma
    • 3
    • 4
  1. 1.School of BusinessCentral South UniversityChangshaChina
  2. 2.School of Management Science and EngineeringNanjing University of Information Science and TechnologyNanjingChina
  3. 3.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain
  4. 4.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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