AbstractThe concept of ranking fuzzy numbers has received significant attention from the research community due to its successful applications for decision making. It complements the decision maker exercise their subjective judgments under situations that are vague, imprecise, ambiguous and uncertain in nature. The literature on ranking fuzzy numbers show that numerous ranking methods for fuzzy numbers are established where all of them aim to correctly rank all sets of fuzzy numbers that mimic real decision situations such that the ranking results are consistent with human intuition. Nevertheless, fuzzy numbers are not easy to rank as they are represented by possibility distribution, which indicates that they possibly overlap with each other, having different shapes and being distinctive in nature. Most established ranking methods are capable to rank fuzzy numbers with correct ranking order such that the results are consistent with human intuition but there are certain circumstances where the ranking methods are particularly limited in ranking non – normal fuzzy numbers, non – overlapping fuzzy numbers and fuzzy numbers of different spreads.
As overcoming these limitations is important, this study develops an intuition based decision methodology for ranking fuzzy numbers using centroid point and spread approaches. The methodology consists of ranking method for type – I fuzzy numbers, type – II fuzzy numbers and Z – numbers where all of them are theoretically and empirically validated. Theoretical validation highlights the capability of the ranking methodology to satisfy all established theoretical properties of ranking fuzzy quantities. On contrary, the empirical validation examines consistency and efficiency of the ranking methodology on ranking fuzzy numbers correctly such that the results are consistent with human intuition and can rank more than two fuzzy numbers simultaneously. Results obtained in this study justify that the ranking methodology not only fulfils all established theoretical properties but also ranks consistently and efficiently the fuzzy numbers. The ranking methodology is implemented to three related established case studies found in the literature of fuzzy sets where the methodology produces consistent and efficient results on all case studies examined. Therefore, based on evidence illustrated in this study, the ranking methodology serves as a generic decision making procedure, especially when fuzzy numbers are involved in the decision process.
|Date of Award||Aug 2015|
|Supervisor||Alexander Gegov (Supervisor), Mohamed Bader-El-Den (Supervisor) & Janka Chlebikova (Supervisor)|