ABSTRAaAs a method of solving multipkcriteria decision making problems with a single quantitatiw objective and multiple qualitative objeaiws, the post-modd adysis (PMA) approach is proposed. The eSSena of PMA is to support the trade-offs M a n a quantitative objective and multiple qualitative objectives so that the decision maker can find a perceived most p r c f e d nondominated solution. Tb this end, the optimal solution of a quantitative model is found first, without regard for qualitative factors. The solution is then cvaluated in terms of qualitative objeaivts. When the initial quantitatively optimal solution is adjusted to allow improvement of qualitative g~a l g opportunity costs of achieving qualitative goals are incurred. In this proass, an a p a t system and/or gmphical display can be uscd. PMA therefore provides a way to incorporate quantitative models into knowledge-based apert systems. Subject A m Eargahhg Behavior, Dceldon Processes, Decision Supporl Systems, and Sautttvity AMI* INTRODUCIION Among the types of multiplecriteria decision-making (MCDM) problems, multi-objective decision-making (MODM) problems are concerned with those cases that involve a large set of alternatives implicitly defined by constraints as formulated in equation (1). while multiple-attribute decision-making (MADM) problems require choosing from among a small explicit list of alternatives [9]. subject to X E S where X Ci(X) =objective function i, i= 1, . . . , k , S =n-dimensional vector of decision variables = [x 1 g,(X) s bj j = 1, . . . , ml: constraint set. Numerous methods have been developed for the solution of MODM problems. There are few studies, however, that can incorporate qualitative factors in MODM; one exception is the method of alternative generation [ l ] [2]. For cases in whichit is difficult to include all important objectives because of their qualitative nature, this method attempts to generate distinctive alternative solutions out of the feasible solution set of MODM problems. In other words, the MODM problems are converted into MADM problems. The method of alternative generation does not, however, include a formalized framework for considering qualitative factors. To make up for this shortcoming, the attempt to display the hidden attributes in graphical form [16] can be a complementary method. Goal programming with priority 3 34
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