Artificial Intelligence Review

, Volume 52, Issue 3, pp 1873–1927 | Cite as

Pythagorean fuzzy set: state of the art and future directions

  • Xindong PengEmail author
  • Ganeshsree Selvachandran


Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade \(\mu \) and non-membership \(\nu \) satisfying the condition \(\mu ^2+\nu ^2\le 1\). It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Pythagorean fuzzy set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as decision making, aggregation operators, and information measures. Because of such a growth, we present an overview on Pythagorean fuzzy set with aim of offering a clear perspective on the different concepts, tools and trends related to their extension. In particular, we provide two novel algorithms in decision making problems under Pythagorean fuzzy environment. It may be served as a foundation for developing more algorithms in decision making.


Pythagorean fuzzy set Intuitionistic fuzzy set Decision making Aggregation operators Information measures 



The authors are very appreciative to the reviewers for their precious comments which enormously ameliorated the quality of this paper. Our work is sponsored by the National Natural Science Foundation of China (No. 61462019), the General Project of Shaoguan University (No. SY2016KJ11).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.School of Information Science and EngineeringShaoguan UniversityShaoguanChina
  2. 2.Faculty of Business and Information ScienceUCSI UniversityKuala LumpurMalaysia

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