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An (R, S)-norm information measure for hesitant fuzzy sets and its application in decision-making

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Abstract

To characterize the uncertainty of a hesitant fuzzy set, a new entropy, which is called (R, S)-norm information measure, is proposed in this paper. It is proved that the proposed measure satisfies the axiomatic definition of entropy measures for hesitant fuzzy sets, and then, some properties of the proposed measure are also explored. Furthermore, several examples are presented to show the advantages of the (R, S)-norm information measure compared with some existing entropy measures. Then, based on the new information measure, we utilize decision-making method by combining prospect theory with technique for order preference by similarity to an ideal solution to address multi-attribute decision-making problems. Finally, a concrete example of business investment is provided to illustrate the effectiveness of our proposed information measure, and comparative analysis is also completed to verify the validity of the (R, S)-norm information measure.

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Acknowledgements

The authors would like to thank the anonymous referees for helping them refine the ideas presented in this paper and improve the clarity of the presentation. This paper was supported by National Science Foundation of China (Grant Nos: 11671244, 12071271) and the Higher School Doctoral Subject Foundation of Ministry of Education of China (Grant No: 20130202110001).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, Shaanxi, People’s Republic of China

    Chunfeng Suo, Yongming Li & Zhihui Li

  2. School of mathematics, Tonghua Normal University, Tonghua, 134000, Jilin, People’s Republic of China

    Chunfeng Suo

Authors
  1. Chunfeng Suo
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  2. Yongming Li
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  3. Zhihui Li
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Contributions

CS and YL: study conception and design. CS and YL: analysis and interpretation of data. CS and YL: programming. CS, YL, and ZL: drafting of manuscript. CS, YL, and ZL: critical revision.

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Correspondence to Yongming Li.

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Communicated by Regivan Hugo Nunes Santiago.

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Suo, C., Li, Y. & Li, Z. An (R, S)-norm information measure for hesitant fuzzy sets and its application in decision-making. Comp. Appl. Math. 39, 286 (2020). https://doi.org/10.1007/s40314-020-01339-9

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  • DOI: https://doi.org/10.1007/s40314-020-01339-9

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