Communication on the Paper “A Reference-Dependent Regret Model for Deterministic Tradeoff Studies”

This communication focuses on a fundamental problem related to the recently introduced Reference-Dependent Regret Model (RDRM) [Kujawski, 2005] for deterministic multi-criteria decision making. In [Kujawski, 2005] it was asserted that the RDRM model satisfies three properties. The first of these properties, referred to as the “independence of dominated alternatives”, seems to be an intuitive one. According to this property, the RDRM model preserves the ranking of two alternatives Ai and Aj with ranking Ai Afj when a new alternative dominated by Ai is introduced or an old alternative dominated by Aj is dropped. In this communication it is demonstrated algebraically and also by means of a numerical example that the RDRM model may fail to satisfy this property. The implication is that when the concepts of regret and/or rejoicing are considered and defined in terms of all the available alternatives in accordance with the RDRM, adding or dropping a dominated alternative can change the ranking of the alternatives and violate the independence of dominated alternatives property

A study of regret and rejoicing and a new MCDM method based on them

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 controversial problem is that some well-known MCDM methods, like the additive AHP methods and the ELECTRE II and III methods, may cause some types of rank reversal problems. Rank reversal means that the ranking between two alternatives might be reversed after some variation occurs to the decision problem, like adding a new alternative, dropping an old alternative or replacing a non-optimal alternative by a worse one etc. Usually such a rank reversal is undesirable for decision-making problems. If a method does allow it to happen, the validity of the method could be questioned. However, some recent studies indicate that rank reversals could also happen because of people’s rational preference reversal which may be caused by their emotional feelings, like regret and rejoicing. Since regret and rejoicing may play a pivotal role in evaluating alternatives in MCDM problems, sometimes the decision maker (DM) may want to anticipate these emotional feelings and consider them in the decision-making process. Most of the regret models in the literature use continuous functions to measure this emotional factor. This dissertation proposes to use an approach based on a linguistic scale and pairwise comparisons to measure a DM’s anticipated regret and rejoicing feelings. The approach is shown to exhibit some key advantages over existing approaches. Next a multiplicative MCDM model is adopted to aggregate the alternatives’ associated regret and rejoicing values with their performance values to get their final priorities and then rank them. A simulated numerical example is used to illustrate the process of the proposed method. Some sensitivity analyses which aim at examining how changes of regret and rejoicing values might affect the ranking results of the decision problems are also developed. Then a fuzzy version of the new method is introduced and illustrated by a numerical example. Finally, some concluding remarks are made. Ranking intransitivity and some other issues about the proposed method are analyzed too