Earlier studies on multiple criteria decision making (MCDM) with imprecise information can be found in a range of literatures and some authors refer to it as incomplete information, partial information, linear partial information (LPI) or incomplete k ...
Earlier studies on multiple criteria decision making (MCDM) with imprecise information can be found in a range of literatures and some authors refer to it as incomplete information, partial information, linear partial information (LPI) or incomplete knowledge. It is said that the need for handling imprecise data occurs in situations such as time pressure or lack of data, intrinsically intangible or non-monetary nature of criteria, a decision maker’s limited attention and information processing capability, and the like. As Barron and Barrett (1996) stated, for example, various methods for eliciting exact weights from the decision maker may suffer on several counts because the weights are highly dependent on the elicitation method (Shoemaker and Waid 1982, Jaccard et al. 1986, Borcherding and von Winterfeldt 1988, Fischer 1995) and there is no agreement as to which method produces more accurate results. In some cases, imprecise information can be utilized when many alternatives are available in a decision problem, and evaluating all of them in detail is not practical and thus allow an efficient preliminary evaluation for the identification of the more promising alternatives to be studied in detail (Kirkwood and Sarin 1985). On one hand, allowing for imprecision of preference information may provide the decision maker with the freedom to choose how to express preferences and convenience of an assessment procedure which matches some people’s natural way of thinking. It may, on the other hand cause, decision analysts difficulties in establishing dominance relations among alternatives from the viewpoint of the second phase. When assuming the underlying evaluation model is an additive multiattribute value (MAV) model, an aggregation method with imprecise attribute weights requires using linear programs to identify the most preferred alternative due to the fact attribute weights range over a pre-specified weight region. In a case where the weights are known to the decision maker only ordinally, the alternative which has the maximum a multiattribute value, is the best alternative to implement when the alternatives are evaluated on the basis of extreme points of a weight region. The problem is, however, the number of final decision results available may be more than one. Further interactions with the decision maker for eliciting specific attribute weights or narrowing down the existent range of weights can be used for reduction of the number of available alternatives, which sometimes fails to produce a single best alternative. With regard to this, approximate weights that satisfy the ordinal rank order of attribute weights can be considered as an option for aiding a multiattribute decision analysis and a variety of well-established rank-based weights methods have been proposed and evaluated (Stillwell et al. 1981, Barron and Barrett 1996, Jia et al. 1998). In this paper, a weighting method, which is originated by other discipline than decision analysis, is presented and its performance is compared with other approximate weights methods via simulation.