Applied Intelligence

, Volume 49, Issue 3, pp 837–857 | Cite as

Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations

  • Yuning Zhang
  • Jie Tang
  • Fanyong MengEmail author


Interval-valued hesitant fuzzy preference relations (IVHFPRs) are useful that allow decision makers to apply several intervals in [0, 1] to denote the uncertain hesitation preference. To derive the reasonable ranking order from group decision making with preference relations, two topics must be considered: consistency and consensus. This paper focuses on group decision making with IVHFPRs. First, a multiplicative consistency concept for IVHFPRs is defined. Then, programming models for judging the consistency of IVHFPRs are constructed. Meanwhile, an approach for deriving the interval fuzzy priority weight vector is introduced that adopts the consistency probability distribution as basis. Subsequently, this paper builds several multiplicative consistency-based programming models for estimating the missing values in incomplete IVHFPRs. A consensus index is introduced to measure the agreement degree between individual IVHFPRs, and a method for increasing the consensus level is presented. Finally, a multiplicative consistency-and-consensus-based group decision-making method with IVHFPRs is offered, and a practical decision-making problem is selected to show the application of the new method.


Group decision making IVHFPR Multiplicative consistency Consensus Programming model 



This work was supported by 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 State Key Program of National Natural Science of China (No. 71431006), and the Hunan Province Foundation for Distinguished Young Scholars of China (No. 2016JJ1024).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Management and EconomicsBeijing Institute of TechnologyBeijingChina
  2. 2.School of BusinessCentral South UniversityChangshaChina
  3. 3.School of Management and EconomicsNanjing University of Information Science and TechnologyNanjingChina

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