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Perception based functions with boundary conditions

The methods of reconstruction of perception based functions (PBF) given by the set of rules like “If X is SMALL then Y is VERY QUICKLY INCREASING”, “If X is BETWEEN A and B then Y is SLOWLY DECREASING” are considered. Such set of rules may be considered as a linguistic description of derivative. Fuzzy functions reconstructed from such description may be considered as solutions of correspondent differential equation. The methods of reconstruction of PBF based on an initial value and on boundary conditions are described. The second case is formulated as an optimization problem and results of solution of this problem are discussed.