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Research on Normal Pythagorean Neutrosophic Set Choquet Integral Operator and Its Application

Changxing Fan1, Jihong Chen2,*, Keli Hu1,3, En Fan1, Xiuqing Wang1
1 Department of Computer Science, Shaoxing University, Shaoxing, China
2 College of Management Shenzhen University, Shenzhen, China
3 Information Technology R&D Innovation Center of Peking University, Shaoxing, China
* Corresponding Author: Jihong Chen. Email:
(This article belongs to this Special Issue: Extension, Modeling and Applications of Fuzzy Set Theory in Engineering and Science)

Computer Modeling in Engineering & Sciences 2022, 131(1), 477-491.

Received 06 September 2021; Accepted 26 October 2021; Issue published 24 January 2022


We first propose the normal Pythagorean neutrosophic set (NPNS) in this paper, which synthesizes the distribution of the incompleteness, indeterminacy, and inconsistency of the Pythagorean neutrosophic set (PNS) and normal fuzzy number. We also define some properties of NPNS. For solving the decision-making problem of the non-strictly independent and interacting attributes, two kinds of NPNS Choquet integral operators are proposed. First, the NPNS Choquet integral average (NPNSCIA) operator and the NPNS Choquet integral geometric (NPNSCIG) operator are proposed. Then, their calculating formulas are derived, their properties are discussed, and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied. Finally, the two kinds of operators are applied to validate the stability of the new method.


Normal pythagorean neutrosophic set (NPNS); NPNS choquet integral average (NPNSCIA) operator; NPNS choquet integral geometric (NPNSCIG) operator; multi-attribute decision making (MADM)

Cite This Article

Fan, C., Chen, J., Hu, K., Fan, E., Wang, X. (2022). Research on Normal Pythagorean Neutrosophic Set Choquet Integral Operator and Its Application. CMES-Computer Modeling in Engineering & Sciences, 131(1), 477–491.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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