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Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making

Author

Listed:
  • Xunjie Gou

    (Sichuan University)

  • Zeshui Xu

    (Sichuan University)

Abstract

Intuitionistic fuzzy numbers (IFNs) have already been applied to many fields, especially in multi-attribute decision making (MADM). Based on the basic operational laws and information aggregation methods of IFNs, MADM with intuitionistic fuzzy information has become more and more popular. In this paper, we investigate the MADM problems where the attribute values take the form of interval numbers and the weight information on the attributes are expressed as IFNs. We first propose a novel exponential operational law based on IFNs and interval numbers, and then study some of its desirable properties. Based on the exponential operational law, we put forward an intuitionistic fuzzy weighted exponential aggregation operator, and utilize it to develop a MADM method. Finally, we apply our method to solve the decision making problem under uncertainty.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:2:d:10.1007_s10700-016-9243-y
    DOI: 10.1007/s10700-016-9243-y
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    References listed on IDEAS

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    1. Zeshui Xu, 2015. "Uncertain Multi-Attribute Decision Making," Springer Books, Springer, edition 127, number 978-3-662-45640-8, December.
    2. Sun, Bingzhen & Ma, Weimin, 2015. "An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application," Omega, Elsevier, vol. 51(C), pages 83-92.
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    Cited by:

    1. 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.
    2. Xiaohong Chen & Mengjing Wu & Chunqiao Tan & Tao Zhang, 2021. "A random intuitionistic fuzzy factor analysis model for complex multi-attribute large group decision-making in dynamic environments," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 101-127, March.
    3. Ye Tian & Zhibin Deng & Jian Luo & Yueqing Li, 2018. "An intuitionistic fuzzy set based S $$^3$$ 3 VM model for binary classification with mislabeled information," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 475-494, December.
    4. 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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