Comments on “Fuzzy Simulations for Expected Values of Functions of Fuzzy Numbers and Intervals”

Abstract

It must be pointed out that the conclusion about the perfect performance of a recently proposed fuzzy simulation technique for expected values of fuzzy functions by Liu <i>et al.</i> (IEEE Trans. Fuzzy Syst., 29(6), 2021), the <i>improved stochastic discretization algorithm</i> (iSDA), is absolute and dangerous, which requires an urgent correction. Therefore, in this note, first and foremost, several theorems are initiated to address and specify the usage scope of the iSDA, which is related to the type of fuzzy variables involved in the functions. Further, examples and counter-examples with schematic diagrams based on the proposed theorems are provided to illustrate the performance of the iSDA. It is seen that the simulation results of the iSDA would be uncontrollable and lead to unbearable error for counter-examples, which immediately shows the necessity of this note. Second and incidentally, the respective convergence of the iSDA and another algorithm, the <i>special numerical integration algorithm</i> (NIA-S), are proved as supplementary contents for the original paper. Finally, the conclusion about the comparison between the iSDA and NIA-S is also restated.