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Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Author

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  • Zhenghai Ai
  • Xiaoqin Shu
  • Zeshui Xu

Abstract

The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval-valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:3947261
    DOI: 10.1155/2019/3947261
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    References listed on IDEAS

    as
    1. Bin Zhu & Zeshui Xu & Meimei Xia, 2012. "Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, May.
    2. 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.
    3. Xunjie Gou & Zeshui Xu, 2017. "Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 183-204, June.
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