Study On Theory, Methods And Applications For Multiple Attribute Decision-making Problem With Incomplete Information

Multi-attribute decision-making (MADM) is an important branch of decision analysis. It deals with the decision problem with finite set of alternatives and multiple criteria. So far, many methods for solving MADM problem have been developed. But many of these approaches require exact information about decision parameters such as attribute weights and marginal utilities. Although different procedures have been proposed for the evaluation of parameters, it is often impossible to obtain their exact values. Usually, we call such decision problem as multi-attribute decision-making with incomplete information. It is studied and discussed in this dissertation.Chapter 1 surveys the methods developed for solving multi-attribute decision-making problem with incomplete information. These methods are classified into three categories according to the hierarchical structure of attributes and the number of decision-makers. The methods of each category are reviewed based on the incomplete information provided by decision-maker. The existing questions in present works are discussed also.Chapter 2 deals with the consistency and redundancy of information. In multi-attribute decision-making problem with incomplete information, it is difficult for DM to make final decision according to the first incomplete information. So he may provide more new information (i.e. new constraints of parameters). If a new constraint is redundant, then it is void for improving decision. If a new constraint is incompatible with previous ones, then the whole system becomes inconsistent. Therefore, it is very important to judge the consistency and redundancy of information, hi this chapter, we propose the linear and non-linear programming models to check the consistency and redundancy of information and give an approach to make system transform from inconsistency to consistency by abbreviating the incompatible constraints. Further, an extension is made to hierarchical structure. Above results are proved also.Chapter 3 proposes the model and method for multi-attribute decision-making with incomplete and uncertainty information. Incomplete information means that decision-maker may not evaluate marginal utilities exactly, only provide their partial order relations. Uncertainty means that decision-maker is not sure the exactness of partial order relations. This chapter presents a model to describe multi-attribute decision-making with incomplete and uncertainty information, and gives a method to deal with such problem. This method aggregates the partial relations with belief structure by evidential reasoning theory, and derives the dominated index and dominating index by the axioms for distance between two preorders. It provides an important tool for coping with the decision-making problem under complex situation.Chapter4 deals with such multi-attribute decision-making problem as: (1) all attributes are organized hierarchically as a tree; (2) it does not require exact evaluation of attribute weights and marginal utilities; (3) it allows the decision-maker to provide parameters constraints through direct comparisons of alternatives. Situation (3) is not discussed in all present works. This chapter deals with such problem. Non-linear programming models are proposed to identify non-dominated and potentially optimal alternatives. By defining new variables, we transformed the non-linear models into the linear model without changing the optimal solution. An indicator is also presented to assist decision-maker to articulate new preferencethat precise values of sample weights do not need to be provided by DM. By using the order with multiples of sample weights, the result of decision- making not only shows the magnitude of attributes, but also shows the growth of attributes.Selecting partner is a critical issue in the formation of virtual enterprise. In chapter 7, following the brief analysis on characteristics of this problem, a mathematical model is built by using the method specifically referred to as evidential reasoning. In this model, each at...