Interactive multi criteria decision making using a Tchebycheff or hybrid utility function and predicted strength of preferences
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Multicriteria Decision Making (MCDM) can provide an efficient means for considering various and conflicting objectives. In this dissertation, we propose a new interactive MCDM method for implicit alternatives to help a Decision Maker (DM) obtain a most preferred solution. In the first method, the Ozbey and Karwan (O-K) method, we use a Tchebycheff function to generate weights consistent with the DM's responses to pairwise comparisons between alternatives. We present a Mixed Integer Linear Programming (MILP) formulation to generate these weights. We improve the O-K method by using the concept of strength of preference and call it the "SOP method". We predict a DM's degree of preference among alternatives and use this predicted value in an MILP formulation to generate multipliers for a Tchebycheff function which are consistent with the DM's responses to pairwise comparisons. We aim to improve the performance of our previous method by generating better alternatives and asking fewer questions with the same level of information indicating an increase in efficiency. We also extend our previous approach by developing a Weight Generator (WG) model which approximates the DM's utility function by a hybrid Tchebycheff/linear function. We attempt to show that this approximation is a better representation than a pure Tchebycheff function approximation. We believe this is the first attempt to approximate the DM's utility function by a hybrid function which is a distinguishable contribution to the literature. Finally, we present our last method (Hybrid SOP) in which we combine the hybrid and SOP approaches. We aim to find out the combined effect of the two approaches. We test our approaches with different true utility functions on various sized multiple criteria linear programming problems. The computational results show that even with non-Tchebycheff true utility functions, the O-K method can generate alternatives very close to the optimal solution with relatively few questions. The comparison of our results with other methods reveals the advantage of our approach. The comparison of the methods reveals that the SOP method generates better alternatives than the O-K method with less number of questions. We show that the Hybrid method works better than the Tchebycheff approximation when the true utility function is linear, quadratic, or fourth order and does little harm when the true utility function is Tchebycheff.