Capacities on a finite set are sets functions vanishing on the empty set and being monotonic w.r.t. inclusion. Since the set of capacities is an order polytope, the problem of randomly generating capacities amounts to generating all linear extensions of the Boolean lattice. This problem is known to be intractable even as soon as $n>5$, therefore approximate methods have been proposed, most notably one based on Markov chains. Although quite accurate, this method is time consuming. In this paper, we propose the 2-layer approximation method, which generates a subset of linear extensions, eliminating those with very low probability. We show that our method has similar performance compared to the Markov chain but is much less time consuming.

翻译：定额数据集上的能力功能在空集中消失,是单调的( w.r. t. ) 。 由于该能力组是一个有顺序的多管区,随机生成能力的问题等于产生布林拉蒂斯的所有线性扩展。 这个问题已知即使一到5美元就难以解决, 因此提出了近似的方法, 主要是基于Markov 链条的方法。 虽然这个方法相当准确, 但很费时。 在本文中, 我们提议了2级近似方法, 产生一个线性扩展子集, 消除概率非常低的扩展。 我们显示, 我们的方法与Markov 链相近, 但花费的时间要少得多 。