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Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers

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Abstract

Intuitionistic fuzzy numbers (IFNs) are a useful tool to depict the uncertain information in real life. Based on IFNs, the intuitionistic fuzzy calculus (IFC) has been put forward recently. To further develop the IFC theory, in this paper, we investigate the limit properties of IFCs, and study the intuitionistic fuzzy infinitesimals and their orders. We also discuss the continuity, the derivatives and the differentials of intuitionistic fuzzy functions in detail, and reveal their relationships. Additionally, we define the metric space of the IFNs, based on which, a series of desirable results are obtained. These results are similar to the ones in the classical calculus.

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Acknowledgments

The authors would like to thank the editors and the anonymous referees for their insightful and constructive comments and suggestions that have led to this improved version of the paper. The work was supported in part by the National Natural Science Foundation of China (Nos. 61273209; 71571123), Natural Science Foundation of Jiangsu Province (No. BK20150721); and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Leshan Normal University, Leshan, 614000, Sichuan, China

    Zhenghai Ai

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

    Zeshui Xu

  3. Collaborative Innovation Center of Social Safety Science and Technology, Nanjing, 210007, Jiangsu, China

    Zeshui Xu

  4. College of Sciences, PLA University of Science and Technology, Nanjing, 210007, Jiangsu, China

    Qian Lei

Authors
  1. Zhenghai Ai
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  2. Zeshui Xu
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  3. Qian Lei
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Correspondence to Zeshui Xu.

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Ai, Z., Xu, Z. & Lei, Q. Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers. Fuzzy Optim Decis Making 16, 71–87 (2017). https://doi.org/10.1007/s10700-016-9239-7

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