International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 943–957 | Cite as

Generalized Pythagorean Fuzzy Maclaurin Symmetric Means and Its Application to Multiple Attribute SIR Group Decision Model

  • Jindong QinEmail author


Pythagorean fuzzy sets, originally proposed by Yager (IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57–61, 2013), which are convenient to describe vagueness and impression in real-world problems, can be regarded as a novel extension of intuitionistic fuzzy sets. Generalized Maclaurin symmetric mean comes as an extension of classical Maclaurin symmetric mean. Their prominent feature is that they can both capture overall interrelationships and also focus on individual importance among the arguments. However, the generalized Maclaurin symmetric mean can only be considered for aggregating numeric information. In this paper, we investigate the generalized Maclaurin symmetric mean and further extend to Pythagorean fuzzy environment. We develop the Pythagorean fuzzy generalized Maclaurin symmetric mean (PFGMSM), the Pythagorean fuzzy weighted generalized Maclaurin symmetric mean (PFWGMSM), and discuss a variety of their desirable properties. To better understand the proposed parameterization operators, we provide an innovative way to extend the classical superiority and inferiority ranking (SIR) group decision model to Pythagorean fuzzy environment. Then, an approach formed with the aid of PFWGMSM and SIR to multiple attribute group decision-making with Pythagorean fuzzy information is developed. Finally, an illustrative example concerning supply chain financial risk decision-making is provided to verify the proposed method and demonstrate its effectiveness.


Pythagorean fuzzy sets Generalized Maclaurin symmetric mean Pythagorean fuzzy generalized Maclaurin symmetric mean Information granularity Multiple attribute group decision-making Multiple attribute group decision-making 



The work was supported by the National Natural Science Foundation of China (NSFC) under Project 71701158, MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project No. 17YJC630114), and the Fundamental Research Funds for the Central Universities 2017VI010.


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of ManagementWuhan University of TechnologyWuhanChina

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