Soft Computing

, Volume 22, Issue 5, pp 1615–1622 | Cite as

On the power sequence of a fuzzy interval matrix with max-min operation

  • Yan-Kuen Wu
  • Chia-Cheng Liu
  • Yung-Yih LurEmail author


An \(n \times n \) interval matrix \({\mathcal {A}}= [\underline{A},\overline{A}]\) is called to be a fuzzy interval matrix if \(0 \le \underline{A}_{ij} \le \overline{A}_{ij}\le 1\) for all \(1 \le i, j \le n\). In this paper, we proposed the notion of max-min algebra of fuzzy interval matrices. We show that the max-min powers of a fuzzy interval matrix either converge or oscillate with a finite period. Conditions for limiting behavior of powers of a fuzzy interval matrix are established. Some properties of fuzzy interval matrices in max-min algebra are derived. Necessary and sufficient conditions for the powers of a fuzzy interval matrices in max-min algebra to be nilpotent are proposed as well.


Interval matrix Max-min algebra Convergence Nilpotence 



The first author’s research is supported in part by MOST 104-2410-H-238-003. The third author’s research is supported in part by MOST 104-2115-M-238-001.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Business AdministrationVanung UniversityTaoyuanTaiwan, ROC
  2. 2.Department of Industrial ManagementVanung UniversityTaoyuanTaiwan, ROC

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