Classification based on 3-similarity

Similarity concept, finding the resemblance or classifying some groups of objects and study their common properties has been the interest of many researchers. Basically, in the studies the similarity between two objects or phenomena, 2-similarity in our words, has been discussed. In this paper, we consider the case when the resemblance or similarity among three objects or phenomena of a set, 3-similarity in our terminology, is desired. After defining 3-equivalence relation and 3-similarity, some common and different points between them are investigated. We will see that in some special cases we can reach from 3-similarity to 2-similarity.