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The Basis and Coordinates in Intuitionistic Fuzzy Environment

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Abstract

In 1983, Atanassov extended the fuzzy set and originally introduced the concept of intuitionistic fuzzy set (IFS). The basic elements in every IFS are called intuitionistic fuzzy numbers, each of which consists of a membership degree, a non-membership degree and a hesitancy degree. Compared with the traditional fuzzy set, the IFS is more flexible and practical to deal with the ambiguity and uncertainty. In this paper, we first try to define the basis in intuitionistic fuzzy environment and then study some of its relevant properties. After that, we propose the coordinates based on the basis and present some theorems of the coordinates. Finally, we show how to find the smallest basis of any region.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. 71571123 and 71771155).

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Authors and Affiliations

  1. College of Sciences, The Army Engineering University of PLA, Nanjing, 210007, Jiangsu, China

    Rufei Ma, Shousheng Liu & Qian Lei

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

    Zeshui Xu

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  1. Rufei Ma
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  2. Shousheng Liu
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  3. Zeshui Xu
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Correspondence to Zeshui Xu.

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Ma, R., Liu, S., Xu, Z. et al. The Basis and Coordinates in Intuitionistic Fuzzy Environment. Int. J. Fuzzy Syst. 20, 1483–1494 (2018). https://doi.org/10.1007/s40815-018-0469-4

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  • DOI: https://doi.org/10.1007/s40815-018-0469-4

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