This paper gives and justifies a practical approach for solving fuzzy singular integro-differential equations. First, by using different techniques, we show that solutions to two types of fuzzy singular integro-differential equations exist and are unique: Picard’s theorem for logarithmic kernels and Arzelà–Ascoli theorem for Cauchy ones. Then, utilizing airfoil polynomials, we provide a collocation method to solve the current problems numerically. We also look at the approximate equations’ solutions, and we introduce the concept of error analysis. Using new procedures, we obtain two systems of linear equations. These are the problems to be examined. Eventually, we exhibit the precision of the proposed approach via numerical examples.