Efficient methods for verifying monotonicity of 2-additive fuzzy measures

We develop numerically efficient methods for verifying monotonicity of 2-additive fuzzy measures. The problem is translated to verifying if a point in a high dimensional space belongs to a polytope. We take advantage of compact vertex representation of the polytope of 2-additive fuzzy measures and show polynomial solvability of that problem, as opposed to verifying an exponentially large number of linear inequalities. We formulate a method based on linear programming which is several orders of magnitude more efficient than the baseline, and then further reduce the set of inequalities and present a method with linear complexity relative to the dimension of the underlying vector space. The methods presented are benchmarked numerically.