The card sorting problem involves the similarity judgments of pairs of photos, taken from a set of photos, by a group of participants. Given the lack of an objective standard for judging similarity, different participants may be using different strategies in judging the similarity of photos. It could be very useful to identify and study these strategies. In this paper, we present a framework for three-way analysis of judgments of similarity. Based on judgments by the set of participants, we divide all pairs of photos into three classes: a set of similar pairs that are judged by at least 60% of participants as similar; a set of dissimilar pairs that are judged by at least 60% of participants as dissimilar; and a set of undecidable pairs that have conflicting judgments. A more refined three-way classification method is also suggested based on a quantitative description of the quality of similarity judgments. The classification in terms of three classes provides an effective method to examine the notions of similarity, dissimilarity, and disagreement.