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

Energy Discriminant Analysis, Quantum Logic, and Fuzzy sets