The paper consists of two parts: (1) a decision-support system (DSS) for discrete multiple criteria decision-making (MCDM) problems; and (2) a heuristic interactive approach when the decision-maker (DM) responds to paired comparisons of alternatives. In the DSS, the DM is provided with flexibility in terms of using different approaches, different assumptions, and manipulating and controlling the solution procedure in a very simple and convenient way. In the interactive approach it is assumed that the DM wishes to maximize an unknown quasiconcave utility function for discrete MCDM problems. Several heuristic procedures are developed for ranking and eliminating alternatives, assuming that the DM can make paired comparisons and indicate strength of preference. An interactive paired comparison method is developed using these heuristics and a gradient-based procedure. Heuristic approaches for finding local adjacent discrete points to approximate the gradient and for identifying discrete points for the one-dimensional search are discussed.