A prescriptive or normative approach, multi-attribute decision- making, simply denoted MADM, technique is a well-known tool in decision analysis. In the 1970's, research focused on the theory and procedures of MADM, thus yielded many number of methodologies. Much of these approaches requires cardinal or numerical data.
However, to achieve such cardinal information from the decision maker (DM) would be very difficult and require considerable cognitive burden on the DM. Thus, more reasonable approaches are required for MADM or MADM support in such a manner that the DM can provide his/her knowledge in a comfortable mind. The motivation a new approach should be developed is come from the requirement.
Since the 1980's, emphasis has shifted toward to find out the behavioral foundations of decision-making and to support the entire decision-making process from problem formulation through solution implementation. Particularly interactive procedures have moved to center stage in recent years, for being able to aid the entire MADM process.
A key feature of MADM is that the DM is willing or able to provide only incomplete parameter value information, because of time pressure and lack of knowledge. These can take the form of linear inequalities such as rankings, interval descriptions, and so on. If the parameter value information is precisely assessed by the DM, then an optimal decision can be easily made.
With the imprecisely 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 MADM support. The aim of this thesis is to present tools or techniques for the MADM support with incomplete information. Moreover a practical application is shown, and further a method for the development of MADM support system is discussed.
In this thesis, we first describe a number of classical and traditional approaches for MADM and their shortcomings. Incomplete information is defined, and an interactive procedure is presented as a framework for MADM support with incomplete information. We will present solution techniques for each step of the interactive procedure as follows:
We present a mathematical programming model for establishing pairwise dominance relationships with incomplete information, which model is based on linear additive weighting. Some techniques for solving the model under certainty and uncertainty are provided. An additional dominance, weak dominance, theory is presented. When the DM is not willing or able to provide more information on parameters, the weak dominance technique is useful for a final choice-making.
We provide a guideline on assessing incomplete parameter value information. We also suggest a dominance graph and propose an algorithm of generating the dominance graph based on a graph theory algorithm. This graph is a pictorial representation of the ordinal preferences of alternatives as determined from the solution of mathematical programming models. The dominance graph can encourage rank-ordering alternatives and aiding the selection of preferable alternatives, since it can compactly display the dominance structure of all alternatives.
Using the methods proposed, we will examine an application to management evaluation of a firm that has a number of branch offices. The management evaluation represents the performance of all tasks or some key tasks is appraised. The task can be viewed as attributes. This firm is going to rank-order his branch offices, alternatives, according to their performance with respect to their common multiple attributes. In addition, the firm is willing and able to provide incomplete preference information on attribute weights and utilities. Thus the firm's problem becomes a MADM model with incomplete information. We demonstrate how to use the proposed methods in order to solve the MADM problem.
Finally, some conclusions are contained, where a summary of contributions and a direction of further studies are presented. A major contribution is in reducing the information burden on the DM, and thus providing practical assistance to the DM. As a future study, we will discuss an issue for the development of MADM support system.
