Training the fuzzy integral

The value of the fuzzy integral in a decision making environment where uncertainty is present has been well established. The fusion of multiple information sources is very valuable in overcoming the inherent ambiguities present in single information sources and in resolving conflicting information from separate decisions. However using the fuzzy integral to overcome such uncertainties introduces an uncertainty of its own, specifically that of generating the importance of each subset of the information sources in determining an unambiguous solution. In this paper, a neuron model for using the fuzzy integral in a multiclass decision making environment is presented. A method of training the fuzzy density values from labeled data is developed. This training algorithm uses a reward and punishment scheme in order to increase the reliability of the decision making process. The result of this training is a set of fuzzy density values which represents the importance of each source with respect to the decision. One important feature of this method is that the fuzzy density values for all classes are considered at each iteration, resulting in more comparable values for the fuzzy integrals, a troublesome problem with many independent training algorithms. The training algorithm is demonstrated with synthetic data and in an automatic target recognition application.