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Exponential operations of interval-valued intuitionistic fuzzy numbers

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Abstract

The operational laws of intuitionistic fuzzy numbers are useful in dealing with the problems under intuitionistic fuzzy circumstances. As a supplementation, the exponential operational law of intuitionistic fuzzy numbers has been defined. Consider that we may utilize interval-valued intuitionistic fuzzy numbers (IVIFNs) to express uncertain weight information comprehensively in the complex multi-attribute decision making problems, in this paper, we discuss two exponential operational laws of IVIFNs, namely, the exponential operational law of IVIFNs with crisp parameter and the exponential operational law of IVIFNs with interval-valued parameter. Several properties and aggregation methods based on the exponential operational laws are discussed. Furthermore, we propose a new method to compare the novel dual interval-valued intuitionistic fuzzy numbers. Additionally, we give two information aggregation methods over these two exponential operational laws for dealing with some special problems in multi-attribute decision making, and finally, we apply the methods to a practical problem involving the choice of the optimal powered roof support for coal extraction with a high recovery rate.

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Acknowledgments

This research was funded by the National Natural Science Foundation of China (No. 61273209), and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

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Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610064, China

    Xunjie Gou, Zeshui Xu & Huchang Liao

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  1. Xunjie Gou
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  2. Zeshui Xu
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  3. Huchang Liao
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Correspondence to Zeshui Xu.

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Gou, X., Xu, Z. & Liao, H. Exponential operations of interval-valued intuitionistic fuzzy numbers. Int. J. Mach. Learn. & Cyber. 7, 501–518 (2016). https://doi.org/10.1007/s13042-015-0434-6

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  • DOI: https://doi.org/10.1007/s13042-015-0434-6

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