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This paper investigates rational harmonically mode-locked fiber ring lasers generating amplitude-stabilized fourth-order optical pulse trains at 13.91 GHz using a modulation signal frequency of 3.477 GHz. Pulse amplitude stabilization in terms of both amplitude equality and low amplitude noise is realized by using the nonlinear characteristics of a Mach-Zehnder intensity modulator in conjunction with intracavity optical filtering. The generated optical pulse trains are investigated for their amplitude equalization, amplitude noise, supermode noise suppression, and pulse timing jitter. It is shown that the pulses remained close to transform-limited over an operating wavelength range of 1535-1565 nm.