Higher-order partial derivatives of uncertain field with application to higher-order uncertain partial differential equation

Binhao He () and Baoding Liu ()
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Binhao He: Tsinghua University
Baoding Liu: Tsinghua University

Fuzzy Optimization and Decision Making, 2025, vol. 24, issue 2, No 7, 317-342

Abstract: Abstract Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper revises the definition of first partial derivatives of uncertain field and defines higher-order partial derivatives for the first time. Then some sufficient and necessary conditions for uncertain fields possessing partial derivatives are derived. Finally, some examples are documented to verify the solution of higher-order uncertain partial differential equation.

Keywords: Uncertainty theory; Uncertain calculus; Uncertain differential equation; Partial derivative (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10700-025-09448-y

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