Comparing methods for multiattribute decision making with ordinal weights

Abstract

This paper is concerned with procedures for ranking discrete alternatives when their values are evaluated precisely on multiple attributes and the attribute weights are known only to obey ordinal relations. There are a variety of situations where it is reasonable to use ranked weights, and there have been various techniques developed to deal with ranked weights and arrive at a choice or rank alternatives under consideration. The most common approach is to determine a set of approximate weights (e.g., rank-order centroid weights) from the ranked weights. This paper presents a different approach that does not develop approximate weights, but rather uses information about the intensity of dominance that is demonstrated by each alternative. Under this approach, several different, intuitively plausible, procedures are presented, so it may be interesting to investigate their performance. These new procedures are then compared against existing procedures using a simulation study. The simulation result shows that the approximate weighting approach yields more accurate results in terms of identifying the best alternatives and the overall rank of alternatives. Although the quality of the new procedures appears to be less accurate when using ranked weights, they provide a complete capability of dealing with arbitrary linear inequalities that signify possible imprecise information on weights, including mixtures of ordinal and bounded weights.