Development of methods for multiple criteria decision support under incomplete information and hierarchical structure

Abstract

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 forms 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 emphasized is that the first formulation for checking dominance and potential optimality becomes a nonlinear programming problem and hence cannot be treated by standard methods without further elaboration. This is because we have to deal with partially known information on both attribute weights and marginal values so that sum-product forms of variables are involved in the model. We thus provide how this problem is transformed into a linear programming equivalent. A change of variable technique is utilized in this transformation. Also, introducing dummy variable enables us to extend the developed techni...