Extending Malakooti's model for ranking multicriteria alternatives with preference strength and partial information

The paper deals with a multiple attribute decision making methodology when a decision maker (DM) specifies her/his preferences in imprecise ways, which is basically an extended version of Malakooti's prior work. Usually, it is said that the DM is willing, or able, to provide partial information, because of time pressure, lack of domain knowledge, or data and the like. In this paper, we consider two categories of partial preference information. First, partial information is related to holistic preference judgments about some pair of alternatives. Second, in a situation where the characteristics of some attributes considered are abstract, or noncommensurate, it is sometimes difficult to make an exact performance evaluation of alternatives with respect to those attributes. To circumvent this difficulty, we allow the DM to specify partial information on performance evaluations, which is similar to the types of preference judgments on some pairs of alternatives. Prioritizing multiple attribute alternatives under two categories of partial information causes an intractable nonlinear program, which is the first issue we try to resolve in the paper. We further propose a measure of preference strength as a decision rule. With partial information, often the use of strict dominance rule yields a larger number of nondominated candidates than the DM wants. Assume a situation where the DM is not willing to provide additional information to reduce the number of nondominated candidates, but she/he wants to have a single optimal candidate or rank ordering of alternatives. It is then necessary to develop a method like one we propose as a preference strength measure.