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Sugeno Integral of Set-Valued Functions with Respect to Multi-submeasures and Its Application in MADM

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Abstract

Based on theoretical analysis of fuzzy integrals, this paper firstly defines the Sugeno integral of set-valued mappings with respect to multi-submeasures, which is an extension of Sugeno integrals of single-valued mappings and Sugeno integrals of set-valued mappings with respect to fuzzy measures. Some desirable properties and the computing rule of it are also discussed and proved in this paper. Then, a novel multi-attribute decision-making (MADM) method is established based on the computing rule of the Sugeno integral defined in this paper under an interval-valued hesitant fuzzy environment, in which all values assigned to alternatives, experts and attributes are all expressed by interval-values. Finally, a numerical MADM example is established to verify the practicality and effectiveness of the proposed definition, during the decision process, the positive interaction, negative interaction or non-interaction among attributes can be fully considered.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61573240, 61473239).

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Authors and Affiliations

  1. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an, 710021, China

    Xin Li & Xiaohong Zhang

  2. College of Arts and Sciences, Shanghai Maritime University, Shanghai, 201306, China

    Xin Li & Xiaohong Zhang

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  1. Xin Li
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XL, XZ have contributed equally to this work.

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Correspondence to Xiaohong Zhang.

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Li, X., Zhang, X. Sugeno Integral of Set-Valued Functions with Respect to Multi-submeasures and Its Application in MADM. Int. J. Fuzzy Syst. 20, 2534–2544 (2018). https://doi.org/10.1007/s40815-018-0528-x

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  • DOI: https://doi.org/10.1007/s40815-018-0528-x

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