Sequential representation of fuzzy similarity relations

Abstract

Using a matrix to represent a fuzzy similarity relation has commonly been used in the study of fuzzy relations. Here, we introduce an efficient and compact way to represent similarity relations in the form of a sequence. We shall firstly introduce the notion of the normal form of a membership matrix and then establish an algorithm to obtain the normal form of any given membership matrix of a similarity relation. From the normal form of the matrix, a sequential representation of the similarity relation can be constructed. We shall further discuss the relationship between the matrix representation and the sequential representation of fuzzy similarity relations. Both the algorithm and the construction method will be illustrated by examples. © 1994.