Fuzzy Similarity Relations in Decision Making

What Is Similarity?

Evaluating the similarity between two objects, could be realized by measuring the relationship that links them (Teng et al. 2014). From a mathematical point of view, generally, a relation R is defined between two objects X(x₁,…,x_n) and Y(y₁,…,y_m) by the Cartesian product: R: X×Y → {0,1} where the elements x_i and y_j are either completely related, i.e R(x_i,y_j)=1 or not at all i.e R(x_i,y_j)=0. In such situation, containing two objects only, we talk about a binary relation. If the relation consists of three, four or five objects; then the relation is called ternary, quaternary or quinary (Sivanandam, Sumathi, and Deepa 2007).