In this paper, it is discussed how Zadeh’s extension principle (ZEP) can be used for uncertainty analysis of a system. For this end, basic concepts of the fuzzy mathematics including fuzzy sets, fuzzy numbers and ZEP are briefly presented. A comparison made among the results obtained by the sensitivity analysis, ZEP and Monte Carlo (MC) methods. It is shown that ZEP gives the same outputs as the MC method and is in full agreement with the concept of “uncertainty”. The sensitivity analysis result is not the same as the uncertainty analysis and, often results in smaller range for the output parameters. پرونده مقاله

In this paper, an implicit second order integro-differential equation governing unsteady motion of a solid particle submerged in a fluid medium and, affected by an arbitrary force field is solved numerically. It is assumed that the particle Reynolds number is quite small to use the well-known Basset kernel for the history force. The implicitness and singularity of the equation are removed by using a hybrid quadrature rule (HQR) and a generalized quadrature rule (GQR), respectively. A recursive plan is used to reduce the required CPU time. Two schemes along with the associated numerical solution algorithms are presented. It is described how the accuracy of the method can be increased in a systematic way. The results obtained by several examples show the effectiveness of the method. پرونده مقاله