Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters

This paper proposes a fuzzy interval perturbation method (FIPM) and a modified fuzzy interval perturbation method (MFIPM) for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions. Interval variables are used to quantify the non-probabilistic uncertainty with limited information, whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions. The level-cut method is introduced to decompose the fuzzy parameters into interval variables. FIPM approximates the interval matrix inverse by the first-order Neumann series, while MFIPM improves the accuracy by considering higher-order terms of the Neumann series. The membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem. Three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters, pure interval parameters, and pure fuzzy parameters, respectively. Copyright (C) 2015 John Wiley & Sons, Ltd.