Soft Computing

, Volume 22, Issue 8, pp 2557–2565 | Cite as

On possibility-degree formulae for ranking interval numbers

  • Fang LiuEmail author
  • Li-Hua Pan
  • Zu-Lin Liu
  • Ya-Nan Peng
Methodologies and Application


Since interval numbers are used to evaluate the opinions of decision makers and express the weights of alternatives in various decision making problems, it is requisite to give a feasible method to rank them. In the present paper, the two existing possibility degree formulae for ranking interval numbers are proved to be equivalent. A generalized possibility degree formula is proposed by considering the attitude of decision makers with a prescribed function. Some known possibility degree formulae for ranking interval numbers can be recovered by choosing a special function. The proposed method is applied to uniformly define the weak transitivity of interval multiplicative and additive reciprocal preference relations. Numerical examples are carried out to illustrate the new formula.


Decision making Interval numbers Possibility degree formula Ranking 



The work was supported by the National Natural Science Foundation of China (Nos. 71571054, 71201037), the Guangxi Natural Science Foundation (No. 2014GXNSFAA118013), and the Guangxi Natural Science Foundation for Distinguished Young Scholars (No. 2016GXNSFFA380004).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceGuangxi UniversityNanningPeople’s Republic of China

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