The relations of fuzzy entropy, distance measure, and similarity measure are discussed in this paper. For the purpose of reliable signal selection, the fuzzy entropy is proposed by a distance measure. Properness of the proposed entropy is verified by the definition of the entropy measure. Fourier and Wavelet transform are applied to the stator current signal to obtain the fault features of an induction motor. Membership functions for 3-phase currents are obtained by the Bootstrap method and Central Limit Theorem. Finally, the proposed entropy is applied to measure the fault signal of an induction machine, and the fuzzy entropy values of phase currents are illustrated.