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Novel ranking method of interval numbers based on the Boolean matrix

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Abstract

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.

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Acknowledgements

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.

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Correspondence to Wenyi Zeng or Qian Yin.

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We declare that we have no conflict of interest.

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

Additional information

Communicated by V. Loia.

This work is supported by Grants from the National Natural Science Foundation of China (10971243, 61472043).

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Li, D., Zeng, W. & Yin, Q. Novel ranking method of interval numbers based on the Boolean matrix. Soft Comput 22, 4113–4122 (2018). https://doi.org/10.1007/s00500-017-2625-4

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