Fuzzy Ranking Methods and Their Applications

Fuzzy ranking is a procedure used to compare and order a sequence of fuzzy sets (FSs). It is an essential step in fuzzy decision making problems before a final decision can be drawn. While many fuzzy ranking methods are available in the literature, a generic method that can provide appropriate and satisfactory solutions across a variety of situations has yet to be developed. Many existing methods are limited to rank either type-l fuzzy sets (TIFSs) or interval type-2 fuzzy sets (lT2FSs), and only few methods can flexibility handle both types of FSs. In particular, fuzzy ranking becomes complicated when FSs are represented by possibility distributions, which can overlap with one another. In this thesis, two new fuzzy ranking methods with different purposes are proposed. The first method ranks both TIFSs and IT2FSs by considering ranking and weighting issues, while the second ranks both TIFSs and IT2FSs by integrating decision makers' viewpoints. Besides that, it is important for a fuzzy ranking method to satisfy a set of reasonable fuzzy ordering properties. As a result, the capability of the proposed fuzzy ranking methods in fulfilling the relevant properties is analyzed and discussed. The usefulness of both methods is demonstrated using real-world applications. The results positively indicate efficacy of the proposed fuzzy ranking methods in solving fuzzy ranking problem as well as complex decision making problems in practical environments