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

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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.

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Acknowledgements

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.

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Correspondence to Yung-Yih Lur.

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The authors declare that there is no conflict of interest.

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Communicated by M. Anisetti.

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Wu, YK., Liu, CC. & Lur, YY. On the power sequence of a fuzzy interval matrix with max-min operation. Soft Comput 22, 1615–1622 (2018). https://doi.org/10.1007/s00500-018-3006-3

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  • DOI: https://doi.org/10.1007/s00500-018-3006-3

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