Fuzzy Similarity Relations in Decision Making

Fuzzy Similarity Relations in Decision Making

Mohamed El Alaoui (National High School for the Arts and Professions, Meknès, Morocco) and Khalid El Yassini (Faculty of Sciences, Moulay Ismail University, Meknès, Morocco)
DOI: 10.4018/978-1-7998-0190-0.ch020

Abstract

Similarity is an ambiguous term that can be interpreted differently depending on the context of use. In this chapter, the authors review some of its uses before focusing on decision making. Ignoring the uncertainty of human knowledge would be denying a major attribute. Thus, they linked it to the fuzzy context. However, even taking this aspect into consideration, the opinion itself must be relevant. Therefore, the more a decision is similar to other opinions, the more it is coherent. Hence, there is a need to measure the similarity between each couple of expressed opinions.
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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,…,xn) and Y(y1,…,ym) by the Cartesian product: R: X×Y → {0,1} where the elements xi and yj are either completely related, i.e R(xi,yj)=1 or not at all i.e R(xi,yj)=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).

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