The expansion of Zadeh-Mamdani method in problems of fuzzy inference on knowledge is considered. A modified method of fuzzy inference is proposed and justified. The proposed method is based on interpretation of components of fuzzy Petri nets as production rules and solving of logical equations in the state space of membership functions of the model, followed by their defuzzification. The process of perceptron learning as procedure of adjusting the weights and shifts to decrease the difference between target and real signals on its output, using a definite tuning (learning) rule is defined. Modified methods of gradient procedures based on the method of back-propagation for multilayer neural networks are developed. Application of the proposed approaches based on advanced hybrid models with solving the problems of fuzzy inference and operative informed decision making allowed to reduce the time to identify, locate and eliminate the causes of failure on the set of alternatives, which is confirmed by experiment. The method appears to be universal in decision-making problems and allows to increase the adequacy of hybrid model and the accuracy of decisions.