The relationship between the switch point on the membership function and the generalized centroid in an interval
type-2 fuzzy set is discussed. A close form representation of the switch point for calculating the endpoint of the generalized centroid is provided in both discrete and continuous conditions. Then an opposite direction searching method for computing the switch point is proposed. The convergence of the switch point is proved. Experimental result shows that the approach is computationally faster than the commonly used Enhanced Karnik-Mendel method without loosing numeric precision.