The probability is the possibility and subjective modeling in scientific research. Mat. and empire. Fundamentals

The mathematical foundations of the theory of measures and necessity as alternative probabilities, credibility and trust as the basis of the mathematical formalism of subjective modeling, integration regarding these measures are considered, their empirical interpretation is given, mathematical methods and algorithms of empirical restoration of measures and integrals, their connection with the probability and mathematical The expectation of and others. As applications, methods are investigated: optimization of solutions, identification, evaluating, forecasting, subjective modeling and interpretation of the measuring experiment, modeling uncertainty and incredible chance, characteristic of subjective judgments and expert conclusions, subjective modeling in the tasks of morphological analysis of images, etc. The book is intended for students and graduate students of physical, mathematical and technical specialties, researchers of mathematical modeling as information technology for obtaining new knowledge