One of the distinctive features pertinent to the present-day conditions under which the power plant equipment operate is the necessity to run it in variable modes, as a result of which certain changes occur in the equipment technical state with time. These factors have generated the need of solving, on a priority basis, a number of unresolved matters concerned with creating models for decision-making and state recognition proceeding from power plant diagnostics with the use of fuzzy information for identifying the equipment state and managing the equipment recovering processes. It should be noted, however, that there is no unified methodological approach to obtaining the relevant information for diagnostic purposes in solving such problems under the conditions of fuzziness and inhomogeneity of initial information about the actual equipment state and its residual life. As a result, the existing methods for shaping data and knowledge in performing an analysis of data and in making managerial decisions are not identified and are not interconnected with their mathematical models. In addition, they are aimed at solving separate tasks and are not always able to ensure that the equipment set model’s parameters are consistent with the actual state of the facility in question. At the same time, the shift that was done in the power industry from the policy of planned and preventive repairs to the policy of repairs according to the actual technical state has resulted in that a higher responsibility has to be undertaken by those who make decisions in determining the repair scope and timeframes, and, accordingly, more stringent requirements are imposed on the quality of diagnostic models. As a consequence of its having been made without doing proper methodical background work, such a shift has lead a situation in which the diagnostic and the decision-making models turned to be inadequate due to the use of information about the equipment state that contains uncertainties. At the same time, recent years have seen a drastically grown interest in various aspects of the intellectual management problem, in particular, the intellectual management by technologies according to a hybrid principle. One of the main areas involves the use of techniques developed within the framework of fuzzy systems and cognitive neural sciences: fuzzy sets, fuzzy logic, fuzzy modeling and management, semantic memory organization, fuzzy mathematics, artificial neural networks, pattern recognition, data processing by human neurons and brain, human consciousness, mind, memory, and artificial life. The article presents the results from extending the range of practical applications of the fuzzy and hybrid system techniques as applied to the technologies of estimating the state of complex technical systems (including power systems), especially under the conditions of data processing and using cognitive neural sciences.