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Partial Derivative and Complete Differential of Binary Intuitionistic Fuzzy Functions

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Abstract

Intuitionistic fuzzy set (IFS), introduced by Atanassov (1986), is the generalization of Zadeh’s fuzzy set. The basic element of IFS is an ordered pair called intuitionistic fuzzy number, based on which, Lei and Xu originally introduced the intuitionistic fuzzy function (IFF) and then developed the derivatives and differentials of IFFs. In the paper, we first define the binary intuitionistic fuzzy numbers (BIFNs) and put forward their operational principles. Then, we discuss the limit and the continuity of sequences of BIFNs. In addition, we study the continuities, the partial derivatives and the complete differentials of the intuitionistic binary fuzzy functions and then generalize the aforementioned definitions and theorems to derive the counterparts of the multivariate intuitionistic fuzzy functions.

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Acknowledgements

The authors thank the anonymous reviewers for their helpful comments and suggestions, which have led to an improved version of this paper. The work was supported by the National Natural Science Foundation of China (No. 71571123) and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

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Authors and Affiliations

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

    Feng Tian, Shousheng Liu & Qian Lei

  2. Business School, Sichuan University, Chengdu, 610065, Sichuan, China

    Zeshui Xu

Authors
  1. Feng Tian
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  2. Shousheng Liu
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  3. Zeshui Xu
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  4. Qian Lei
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Correspondence to Zeshui Xu.

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Tian, F., Liu, S., Xu, Z. et al. Partial Derivative and Complete Differential of Binary Intuitionistic Fuzzy Functions. Int. J. Fuzzy Syst. 19, 273–284 (2017). https://doi.org/10.1007/s40815-017-0300-7

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  • DOI: https://doi.org/10.1007/s40815-017-0300-7

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