Fuzzy systems in high-energy physics

Decision making is one of the major subjects of interest in physics. This is due to the intrinsic finite accuracy of measurement that leads to the possible results to span a region for each quantity. In this way, to recognize a particle type among the others by a measure of a feature vector, a decision must be made. The decision making process becomes a crucial point whenever a low statistical significance occurs as in space cosmic ray experiments where searching in rare events requires us to reject as many background events as possible (high purity), keeping as many signal events as possible (high efficiency). In the last few years, interesting theoretical results on some feedforward connectionist systems (FFCSs) have been obtained. In particular, it has been shown that multilayer perceptrons (MLPs), radial basis function networks (RBFs), and some fuzzy logic systems (FLSs) are nonlinear universal function approximators. This property permits us to build a system showing intelligent behavior , such as function estimation, time series forecasting, and pattern classification, and able to learn their skill from a set of numerical data. From the classification point of view, it has been demonstrated that non-parametric classifiers based FFCSs holding the universal function approximation property, can approximate the Bayes optimal discriminant function and then minimize the classification error. In this paper has been studied the FBF when applied to a high energy physics problem. The FBF is a powerful neuro-fuzzy system (or adaptive fuzzy logic system) holding the universal function approximation property and the capability of learning from examples. The FBF is based on product-inference rule (P), the Gaussian membership function (G), a singleton fuzzifier (S), and a center average defuzzifier (CA). The FBF can be regarded as a feedforward connectionist system with just one hidden layer whose units correspond to the fuzzy MIMO rules. The FBF can be identified both by exploiting the linguistic knowledge available (structure identification problem) and by using the information contained in a data set (parameter estimation problem). The fuzzy system has been found to be effective for the classification tasks of about 2 by 10-3 hadron contamination at 90% of electron acceptance. A comparison between the adaptive system results and the others previous ones obtained by using both statistical and neural network based methodologies also is presented.