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An Extended TOPSIS Method Based on Gaussian Interval Type-2 Fuzzy Set

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Abstract

Compared with trapezoidal interval type-2 fuzzy set (IT2 FS), Gaussian IT2 FS is more concise in representation and can meanwhile capture sufficient uncertainties. Therefore, in this paper the Gaussian IT2 FS is used to model words in multi-attribute decision-making (MADM) process and a comprehensive method is developed under the Gaussian IT2 FS environment. Firstly, a new type of Gaussian IT2 FS is proposed and the ranking rule is constructed to determine the ideal solutions. Secondly, the Euclidean distance is extended to Gaussian IT2 FS to measure the difference between alternatives and ideal solutions. Further, a complete MADM method is established under the framework of TOPSIS (technique for order preference by similarity to an ideal solution). In the end, the effectiveness of the proposed method is illustrated by an investment decision-making example.

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Acknowledgements

The authors would like to appreciate the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that helped to improve the quality of this paper. This work was supported by NSFC Foundation under Grant No. 61402260 and partially supported by the Natural Sciences and Engineering Research Council of Canada through Grant RGPIN-2018-06724.

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Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, **an, 250014, China

    Huidong Wang, **li Yao & Mingguang Dong

  2. School of Computer Science and Technology, Shandong University, **an, 250100, China

    Huidong Wang

  3. CIVC Software Engineering Co. Ltd., **an, 250014, China

    Huidong Wang

  4. Concordia Institute for Information Systems Engineering, Concordia University, Montreal, H3G1M8, Canada

    Jun Yan

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  1. Huidong Wang
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  2. **li Yao
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  3. Jun Yan
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  4. Mingguang Dong
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Correspondence to Huidong Wang.

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Wang, H., Yao, J., Yan, J. et al. An Extended TOPSIS Method Based on Gaussian Interval Type-2 Fuzzy Set. Int. J. Fuzzy Syst. 21, 1831–1843 (2019). https://doi.org/10.1007/s40815-019-00670-6

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  • DOI: https://doi.org/10.1007/s40815-019-00670-6

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