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Total utility of Z-number

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Abstract

Z-numbers, combined with “constraint” and “reliability”, has more power to express human knowledge. How to determine the ordering of Z-numbers and how to make a decision with Z-numbers are both meaningful and open issues. In this paper, a new notion of the total utility of Z-number is proposed to measure the total effects of a Z-number. The proposed total utility of Z-number can be used to determine the ordering of Z-numbers, and can also be simply applied in the application of multi-criteria decision making under uncertain environments. Two particular cases of Z-number (Gaussian and triangular), and some mathematical properties of the total utility of Z-number are discussed in this paper. Several applications and comparative analyses are shown to demonstrate the effectiveness of the proposed total utility of Z-number in the application of ordering Z-numbers and multi-criteria decision making.

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Acknowledgments

The authors greatly appreciate the reviewers’ suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61573290, 61503237), and the China Scholarship Council.

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Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Bingyi Kang & Yong Deng

  2. School of Engineering, University of British Columbia Okanagan, 3333 University Way, Kelowna, BC, V1V 1V7, Canada

    Bingyi Kang & Rehan Sadiq

  3. Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Yong Deng

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  1. Bingyi Kang
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Correspondence to Yong Deng.

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Kang, B., Deng, Y. & Sadiq, R. Total utility of Z-number. Appl Intell 48, 703–729 (2018). https://doi.org/10.1007/s10489-017-1001-5

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