are linear in terms of the decision variables, this variation leads to multiple objective linear programming (MOLP), an important subclass of MCDM problems. There are several definitions that are central in MCDM. Two closely related definitions are those of nondominance (defined based on the criterion space representation) and efficiency (defined based on the decision variable representation). Definition 1. is nondominated if there does not exist another such that and . Roughly speaking, a solution is nondominated so long as it is not inferior to any other available solution in all the considered criteria. Definition 2. is efficient if there does not exist another such that and . If an MCDM problem represents a decision situation well, then the most preferred solution of a DM has to be an efficient solution in the decision space, and its image is a nondominated point in the criterion space. Following definitions are also important. Definition 3. is weakly nondominated if there does not exist another such that . Definition 4. is weakly efficient if there does not exist another such that . Weakly nondominated points include all nondominated points and some special dominated points. The importance of these special dominated points comes from the fact that they commonly appear in practice and special care is necessary to distinguish them from nondominated points. If, for example, we maximize a single objective, we may end up with a weakly nondominated point that is dominated. The dominated points of the weakly nondominated set are located either on vertical or horizontal planes (hyperplanes) in the criterion space. Ideal point: (in criterion space) represents the best (the maximum for maximization problems and the minimum for minimization problems) of each objective function and typically corresponds to an infeasible solution. Nadir point: (in criterion space) represents the worst (the minimum for maximization problems and the maximum for minimization problems) of each objective function among the points in the nondominated set and is typically a dominated point. The ideal point and the nadir point are useful to the DM to get the "feel" of the range of solutions (although it is not straightforward to find the nadir point for design problems having more than two criteria). Illustrations of the decision and criterion spaces The following two-variable MOLP problem in the decision variable space will help demonstrate some of the key concepts graphically. In Figure 1, the extreme points "e" and "b" maximize