An interactive approach for multiple criteria selection problem

In this study, we develop an interactive algorithm for the multiple criteria selection problem that aims to find the most preferred alternative among a set of known alternatives evaluated on multiple criteria. We assume the decision maker (DM) has a quasi-concave value function that represents his/her preferences. The interactive algorithm selects the pairs of alternatives to be asked to the DM based on the estimated likelihood that one alternative is preferred to another. After the DM selects the preferred alternative, a convex cone is generated based on this preference information and the alternatives dominated by the cone are eliminated. Then, the algorithm updates the likelihood information for the unselected pairwise questions. The aim of the algorithm is to detect the most preferred alternative by performing as few pairwise comparisons as possible. We present the algorithm on an illustrative example problem. We also develop a mathematical model that finds the minimum number of questions that can be asked to the DM to determine the most preferred alternative under perfect information. We use the minimum number of questions to develop strategies for interactive algorithm and measure its performance.