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Pythagorean fuzzy inequality derived by operation, equality and aggregation operator

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Abstract

Pythagorean fuzzy set (PFS) is a meaningful generalization of intuitionistic fuzzy set, whose fascinating characteristic is that the sum of square of membership degree \(\mu \), non-membership degree \(\upsilon \) and hesitation degree \(\pi \) is equal to 1 with more flexible value space. Inequality on Pythagorean fuzzy set plays an important role in uncertainty theory. In this paper, we firstly derive some Pythagorean fuzzy inequalities based on some existing operations. Further, based on the existing operations, we develop three Pythagorean fuzzy aggregation operators, including Pythagorean fuzzy square (PFSq), Pythagorean fuzzy arithmetic and Pythagorean fuzzy geometric. Meanwhile, some inequalities on them are profoundly explored. Finally, we construct some Pythagorean fuzzy inequalities by equality \(\mu ^2+\upsilon ^2+\pi ^2=1\) in critical definition and prove them by some existing well-known inequalities, which will provide a new basis for Pythagorean fuzzy inequalities in operations and aggregation operators.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 62006155 and 62102261.

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Authors and Affiliations

  1. College of Computer, National University of Defense Technology, Changsha, 410073, China

    Xindong Peng & Zhigang Luo

  2. School of Information Engineering, Shaoguan University, Shaoguan, 512005, China

    Xindong Peng

Authors
  1. Xindong Peng
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  2. Zhigang Luo
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Contributions

All authors contributed to the study conception and design. Material preparation was performed by Xindong Peng. The first draft of the manuscript was written by Xindong Peng and then polished by Zhigang Luo. All authors read and approved the final manuscript.

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Correspondence to Xindong Peng.

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Peng, X., Luo, Z. Pythagorean fuzzy inequality derived by operation, equality and aggregation operator. Soft Comput 26, 5975–6018 (2022). https://doi.org/10.1007/s00500-022-07078-9

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