Face recognition systems have been in the active research in the area of image processing for quite a long time. Evaluating the face recognition system was carried out with various types of algorithms used for extracting the features, their classification and matching. Similarity measure or distance measure is also an important factor in assessing the quality of a face recognition system. There are various distance measures in literature which are widely used in this area. In this work, a new class of similarity measure based on the Lp metric between fuzzy sets is proposed which gives better results when compared to the existing distance measures in the area with Linear Discriminant Analysis (LDA). The result points to a positive direction that with the existing feature extraction methods itself the results can be improved if the similarity measure in the matching part is efficient.