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

Author

Listed:
  • Zhenghai Ai

    (Leshan Normal University)

  • Zeshui Xu

    (Sichuan University
    Collaborative Innovation Center of Social Safety Science and Technology)

  • Qian Lei

    (PLA University of Science and Technology)

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.

Suggested Citation

  • Zhenghai Ai & Zeshui Xu & Qian Lei, 2017. "Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 71-87, March.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:1:d:10.1007_s10700-016-9239-7
    DOI: 10.1007/s10700-016-9239-7
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    Cited by:

    1. Zhenghai Ai & Xiaoqin Shu & Zeshui Xu, 2019. "Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data," Complexity, Hindawi, vol. 2019, pages 1-14, October.

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