Abstract
Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper defines partial derivatives of uncertain fields for the first time by putting forward the concept of Liu field. Then the fundamental theorem, chain rule and integration by parts of multivariate uncertain calculus are derived. Finally, this paper presents an uncertain partial differential equation, and gives its integral form.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 62073009), the China Postdoctoral Science Foundation (Grant No. 2022M710322), and the National Natural Science Foundation of China (Grant No. 61873329).
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Ye, T. Partial derivatives of uncertain fields and uncertain partial differential equations. Fuzzy Optim Decis Making 23, 199–217 (2024). https://doi.org/10.1007/s10700-023-09417-3
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DOI: https://doi.org/10.1007/s10700-023-09417-3