Possibilistic max-mean dispersion problem

The Max-Mean Dispersion Problem comprises selecting a subset of elements from a set while maximising the average of a measure of dispersion. We usually compute this measure of dispersion based on some distance metric between the elements of the candidate set. However, in real-world applications, this measure of dispersion could be ill-defined or vague. For example, consider the problem of building a team to execute some kinds of project. We can see the dispersion between the members of the team as the team chemistry, so the coach is interested in maximising this chemistry. In this example, it would be very difficult to compute exactly a dispersion measure for each candidate. This is due to the lack of information about how well the candidates worked together in the past. To cope with imprecise or vague information, in this paper, we propose three mixed integer linear programming models based on possibility, necessity, and credibility measures. To the best of our knowledge, this is the first approach which explicitly considers this type of uncertainty in this optimisation problem.