Learning fuzzy measure parameters by logistic LASSO

In this paper, a novel Bayesian hierarchical method is defined by the use of logistic distribution and a Laplacian prior to learn the parameters on fuzzy measures. The new algorithm goes beyond previously published MCE based approaches. It has the advantage that it is applicable to general measures, as opposed to only the Sugeno class of measures. In addition, the monotonicity constraints are handled easily with minimal time or storage requirements. This is made by the use of an alternated sampling to avoid favoring maxlike operators or min-like operators. The use of the logistic distribution eliminates the necessity of using desired outputs, and the Laplacian prior regularize the parameters in the fuzzy measures. Results are given on synthetic and real data sets, the latter obtained from a landmine detection problem.