Study of ranking irregularities when evaluating alternatives by using some ELECTRE methods and a proposed new MCDM method based on regret and rejoicing

Multi-criteria decision-making (MCDM) is one of the most widely used decision methodologies in the sciences, business, and engineering worlds. MCDM methods aim at improving the quality of decisions by making the process more explicit, rational, and efficient. One intriguing problem is that oftentimes different methods may yield different answers to the same decision problem. Thus, the issue of evaluating the relative performance of different MCDM methods is raised. One evaluating procedure is to examine the stability of an MCDM method’s mathematical process by checking the validity of its proposed rankings. The ELECTRE II and III methods are two well-known MCDM methods and widely accepted in solving MCDM problems in civil and environmental engineering. However these two methods have never been studied in detail for the validity of their proposed rankings. Thus, the first aim of this thesis is to examine if these two methods suffer of any type of ranking irregularities and analyze the reasons of the phenomenon. As the research results in this thesis revealed, the ELECTRE II and III methods do allow some types of ranking irregularities to happen. For instance, these two methods might change the indication of the best alternative for a given MCDM problem when one of the non-optimal alternatives was replaced by a worse one. The two methods were also evaluated in terms of two other ranking tests and they failed them as well. Two real-life cases are described to demonstrate the occurrence of rank reversals. Then reasons behind the phenomenon are analyzed. Next an empirical study and some real-life case studies were executed and discussed. The results of these examinations show that the rates of those ranking irregularities were rather significant in both the simulated decision problems and the real-life cases studied in this research. However, some recent studies showed that rank reversals could also happen because people may reverse their preferences due to some emotional feelings, like regret and rejoicing. Thus this thesis proposes a new MCDM method which is based on regret and rejoicing. This new method is expected to satisfy a set of critical conditions.