Soft Computing

, Volume 21, Issue 18, pp 5245–5264 | Cite as

Constructive methods for intuitionistic fuzzy implication operators

  • Yiying Shi
  • Xuehai Yuan
  • Yuchun Zhang


In this paper, two novel constructive methods for fuzzy implication operators are proposed. And they can be used to resolve the questions about how to construct intuitionistic fuzzy implication operators to inference sentence “If x is A, then y is B,” where A and B are intuitionistic fuzzy sets over X and Y, respectively. In the first method, cut sets and representation theorem of intuitionistic fuzzy sets are utilized through triple valued fuzzy implications as well as fuzzy relations to obtain seven intuitionistic fuzzy implication operators. In the second method, the Lebesgue measure of the fuzzy implications with value one and zero is used, and one intuitionistic fuzzy implication operator can be obtained. Finally, properties of those operators are discussed.


Intuitionistic fuzzy implication operators Lebesgue measure Cut sets Fuzzy relation Representation theorem 



This work was supported by the National Science Foundation of China (No. 61473327).

Compliance with ethical standards

Conflict of interest

Yiying Shi, Xuehai Yuan and Yuchun Zhang declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of ScienceShenyang Ligong UniversityShenyangChina
  2. 2.School of ScienceDalian University of Technology at PanjinPanjinChina

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