Interval neutrosophic preference relations and their application in virtual enterprise partner selection

  • Fanyong Meng
  • Na WangEmail author
  • Yanwei Xu
Original Research


How to select satisfactory partners is essential to virtual enterprise and has attracted lots of attention from practitioners and researchers. In many real situations, preference relation is an important structure in representing decision makers’ preference information during the partner selection process. As a special case of neutrosophic sets, interval neutrosophic set (INS) can be used to handle uncertain and inconsistent information in decision making. To show the application, this paper introduces the concept of interval neutrosophic preference relations (INPRs) using interval neutrosophic numbers to denote the true, indeterminacy and false judgments independently. Then, a multiplicative consistency concept for INPRs is proposed to guarantee the ranking accurately. After that, several multiplicative consistency-based nonlinear programming models to derive multiplicatively consistent INPRs and to determine missing values in incomplete INPRs are constructed, respectively. To broaden the application of INPRs, a consensus index based on the distance measure is defined. Meanwhile, an algorithm to group decision making based on INPRs is developed, which can be applied to address incomplete and inconsistent INPRs. Finally, the feasibility and practicability of the developed approach is manifested through an illustrative example, and comparison analysis is performed with several related previous methods about decision making with INSs.


Group decision making Virtual enterprise Interval neutrosophic preference relation Multiplicative consistency 



This work was supported by the National Natural Science Foundation of China (nos. 71571192, 71601049, 71874112, 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 (no. 71790615), and the State Key Program of National Natural Science of China (no. 71431006).

Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaChina
  2. 2.Collaborative Innovation Center on Forecast and Evaluation of Meteorological DisastersNanjing University of Information Science and TechnologyNanjingChina

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