the concepts of similarity and dissimilarity have been the interest of many researchers. basically, in the studies the similarity between two objects or phenomena, has been discussed. in this thesis, we consider the case when the resemblance or similarity among three objects or phenomena of a set, 3-similarity in our terminology, is desired. later we will extend our definitions and propositions to n-similarity. since in some cases recognizing dissimilarity is easier than similarity, we try to find a connection between these relations based on specific functions. we will also define the concept of ?-cuts and relations in connection with the concepts of 3-similarity and 3-equivalence relations. it should mentioned that the related definitions and propositions are on the basis of the generalization of the concepts of the ?-cuts and 3-equivalence relations. at the end, some applications as well as their algorithms will be presented to support our ideas and propositions.

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