Using preference constraints to solve multi-criteria decision making problems

Selecting the best option among a set of alternatives is not always a straightforward process. Usually the alternatives are characterized by several attributes which all need to be considered to some extent when making the final decision. Moreover, each attribute can take several values that could be ranked based on the decision maker's preferences. Of course, we would like to choose the alternative that contains all the highest ranked attributes, but in reality, such an alternative usually does not exist. For example, when buying a car, we would like to buy the car that is the cheapest one and that has the highest safety rating, but the cheapest car usually does not have a high safety rating. The typical approach to solve this problem is to consider every existing combination of attributes and try to rank all the combinations. However, the problem quickly becomes intractable as the number of possible combinations grows exponentially when the number of attributes increases. To tackle this problem, we propose to reduce the search space (i.e., the set of all possible combinations of attributes' values) by discarding the combinations that certainly do not match the decision maker's preferable choice. Our method relies on building preference constraints and on using standard techniques to solve problems with constraints.