An Efficient Algorithm for Sampling Fuzzy Measures

Random generation of fuzzy measures can be viewed as assigning $2^{n}$ ordered random values from the unit interval to the linear extension of power-sets of inputs. Several recently proposed methods for constructing linear extensions have high computational cost. We propose a numerically efficient approach that directly obtains the linear extensions from convex combinations of 0–1 fuzzy measures, reducing the computational complexity to $O(n2^{n})$. The resulting algorithm is very short but is effective in generating a broad range of fuzzy measures as demonstrated by experiments. The full C++ code is presented.