Energy discriminant analysis, quantum logic, and fuzzy sets

In this paper, we show that quantum logic of linear subspaces can be used for recognition of random signals by a Bayesian energy discriminant classifier. The energy distribution on linear subspaces is described by the correlation matrix of the probability distribution. We show that the correlation matrix corresponds to von Neumann density matrix in quantum theory. We suggest the interpretation of quantum logic as a fuzzy logic of fuzzy sets. The use of quantum logic for recognition is based on the fact that the probability distribution of each class lies approximately in a lower-dimensional subspace of feature space. We offer the interpretation of discriminant functions as membership functions of fuzzy sets. Also, we offer the quality functional for optimal choice of discriminant functions for recognition from some class of discriminant functions.