The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.

中文翻译：

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模糊环境下通过欧姆加热倾斜通道的MHD三级流体的数值研究

由于知识不足、实验误差、操作条件和提供不精确信息的参数，会出现不确定性或模糊性。在本文中，我们讨论了在三级流体的三个基本流动问题（即库埃特流、泊肃叶流和库埃特-泊肃叶流）中，清晰和模糊情况下重力和磁性参数的综合影响。带热传递的倾斜通道。具有边界条件的无量纲控制方程被转换为耦合模糊微分方程（FDE）。对于这两种情况，控制方程的模糊形式以及边界条件都是通过使用 MATLAB 中内置的数值技术 bvp4c 求解的，这种方法非常有效且计算成本较低。在第一种情况下，-切割方法，控制模糊不确定性。据观察，模糊的重力和磁参数对于更好的流动和热情况不太敏感。使用三角模糊数 (TFN)，由于所涉及参数的不同值，以表格形式呈现速度和温度曲线的左、右和中值。为了验证，将当前结果与某些特殊情况下的现有结果进行比较，即清晰的情况，发现它们具有良好的一致性。