(A) study on potential optimality for decision support under multiple criteria and incomplete information

Abstract

Most managerial decisions involve choosing an optimal alternative from a number of available alternatives. Researchers have proposed a lot of methods to assist decision makers in choice-making with a set of, usually conflicting, criteria or attributes. Many of these approaches require exact (precise, or complete) information about either or both attribute values and/or trade-off weights. In some practice, however, it is not easy for decision makers to provide such exact data because of, for example, time pressure, lack of knowledge, and including intangible attributes to reflect social and environmental impacts. With the incompletely identified information, however, a selection is not generally made in a single step and some additional information is required to get a final selection. From this point of view, an interactive procedure is required for multi-criteria decision support. The aim of this thesis is to present tools or techniques for the decision support with incomplete information. To address the objective, a mathematical programming model based approach to multi-criteria decision analysis (MCDA) is presented in this thesis when both attribute weights and marginal values are identified incompletely. The incomplete information can take the form of linear inequalities such as rankings, interval descriptions, and so on, which will form a set of constraints in the model. A weighted additive rule is used to evaluate the performance of alternatives. The mathematical programming model presented in this thesis is designated to check whether or not each alternative is outperform for a fixed feasible region denoted by the constraints or incomplete information. The two criteria, dominance and potential optimality, are used to specify outperform alternatives which criteria are well known and encountered in the area of MCDA. Namely, non-dominated and/or potentially optimal alternatives can be regarded as outperform or good alternatives and vice versa. A point to be...