Since pipes with wall-thinning defects can collapse at fluid pressure that are lower than expected, the collapse moment of wall-thinned pipes should be determined accurately for the safety of nuclear power plants. Wall-thinning defects, which are mostly found in pipe bends and elbows, are mainly caused by flow-accelerated corrosion. This lowers the failure pressure, load-carrying capacity, deformation ability, and fatigue resistance of pipe bends and elbows. This paper offers a support vector regression (SVR) model further enhanced with a fuzzy algorithm for calculation of the collapse moment and for evaluating the integrity of wall-thinned piping systems. The fuzzy support vector regression (FSVR) model is applied to numerical data obtained from finite element analyses of piping systems with wall-thinning defects. In this paper, three FSVR models are developed, respectively, for three data sets divided into extrados, intrados, and crown defects corresponding to three different defect locations. It is known that FSVR models are sufficiently accurate for an integrity evaluation of piping systems from laser or ultrasonic measurements of wall-thinning defects.