In this paper we propose the new binary image matching algorithm called the Fuzzy logic induced Hausdorff Distance(FHD) for finding the maximally matched image with the query image. The membership histogram is obtained by normalizing the cardinality of the subset with the corresponding radius after obtaining the distribution of the minimum distance computed by the Hausdroff distance between two binary images. in the proposed algorithm, The fuzzy influence method Center of Gravity(COG) is applied to calculate the best matching candidate in the membership function described above. The proposed algorithm shows the excellent results for the face image recognition when the noise is added to the query image as well as for the character recognition.