Soft Computing

, Volume 22, Issue 12, pp 4113–4122 | Cite as

Novel ranking method of interval numbers based on the Boolean matrix

  • Deqing Li
  • Wenyi ZengEmail author
  • Qian YinEmail author
Methodologies and Application


In this paper, we first analyze several existing ranking approaches for a set of interval numbers which are based on the possibility degree matrix. We show by counterexamples that these methods are not appropriate to rank a set of interval numbers from two viewpoints. Furthermore, we investigate the relationship between the possibility degree matrix and the reciprocal fuzzy preference matrix and analyze the reason that leads to the irrational ranking result. Finally, we propose an improved ranking algorithm for a set of interval numbers based on the Boolean matrix. Two numerical examples and a practical application are provided to illustrate the feasibility and effectiveness of our proposed method.


Interval number Possibility degree Possibility degree matrix Reciprocal fuzzy preference matrix Boolean matrix 



The authors wish to express their gratitude to the anonymous referees and the Editor-in-Chief, Professor Antonio Di Nola, for their kind suggestions and helpful comments in revising the paper.

Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interest.

Ethical approval

This article dees not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.Department of MathematicsShijiazhuang Mechanical Engineering CollegeShijiazhuangPeople’s Republic of China

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