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The chain and substitution rules of interval-valued intuitionistic fuzzy calculus

Author

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  • Yanmin Liu

    (PLA University of Science and Technology)

  • Hua Zhao

    (PLA University of Science and Technology)

  • Zeshui Xu

    (Sichuan University)

Abstract

The interval-valued intuitionistic fuzzy set proposed by Atanassov is the extension of intuitionistic fuzzy set. It extends the membership degree and non-membership to interval values instead of a single value. So it contains more possible values and maybe more considerate. Among all the researches, the exploration on the calculus of interval-valued intuitionistic fuzzy set is entirely new. Recently, Zhao et al. (Int J Comput Intell Syst 9:36–56, 2016) proposed the concept of interval-valued intuitionistic fuzzy function (IVIFF) and gave a calculation method of derivative and differential of IVIFF. Based on this work, in this paper, firstly, we utilize a new and easier method to express the derivative and differential of IVIFF. Secondly, we propose the chain rules of derivative and the form invariance of differential in the interval-valued intuitionistic fuzzy environment. In addition, some properties of the substation rules for interval-valued intuitionistic fuzzy indefinite integrals and definite integrals are also developed.

Suggested Citation

  • Yanmin Liu & Hua Zhao & Zeshui Xu, 2018. "The chain and substitution rules of interval-valued intuitionistic fuzzy calculus," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 265-285, September.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9275-y
    DOI: 10.1007/s10700-017-9275-y
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    References listed on IDEAS

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    1. Joshi, Deepa & Kumar, Sanjay, 2016. "Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(1), pages 183-191.
    2. 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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