불완전정보하의 다요소의사결정을 위한 일반화된 선형계획법

Abstract

This study is concerned with the use of incomplete information on both decision alternative scores and importance weights in multiple attribute decision making (MADM). Incomplete information implies various forms of ordinal and bound data on the alternative scores and weights, which often occurs in practice. In the case of incomplete information, two different mathematical programming models can be built to evaluate the alternatives, both of which become nonlinear programming problems. One scenario seeks to evaluate an alternative in the best scenario for the given incomplete information, also referred as the most optimistic evaluation approach. By contrast, the other scenario seeks the worst scenario, referred as the most pessimistic approach. The earlier work has resolved the optimistic evaluation problem, which transforms the nonlinear model into a linear programming model. However, knowing how to solve the pessimistic evaluation problem remains unclear for MADM with incomplete information. We therefore show in this study that the generalized linear programming techniques can solve the pessimistic evaluation problem, which alters the nonlinear model into a class of linear programming models. This scheme accomplishes a more complete evaluation because the non-dominated alternative evaluated under the worst scenario is superior to the non-dominated alternatives under the best scenario. An application of the software selection problem is also demonstrated.