The paper addresses the task on constructing a method for the identification of complications, arising during oil and gas well drilling, which functions under conditions of an a priori and current uncertainty under the influence of various disturbances, based on the methods of fuzzy sets and fuzzy logic. The methodological approach to assessing the level of complications in the course of oil and gas well drilling, based on the principles of linguistics of the parameters of the drilling process, the linguistics and hierarchy of knowledge about complications in the drilling process, was proposed. We have built mathematical models of the controlled object, which, in contrast to deterministic mathematical models, make it possible to describe in the natural language the cause-effect relations between the parameters of the drilling process and possible complications. These models reflect the logic of an operator’s reasoning with the involvement of non-numeric and fuzzy information by an expert specialist, which makes it possible to formalize the decision-making procedures based on Fuzzy Logic using the parameters and indicators for the process of oil and gas well drilling. The structure of decision support system in controlling the process of well drilling under complicated conditions was proposed. The results of simulation of the developed methods for modeling complications based on the methods of fuzzy sets and fuzzy logic were presented. Their advantages in accuracy in comparison with the known methods in problems of identification of assessment and control under conditions of uncertainty about the structure and parameters of the object were shown. The actual complications were detected whose elimination would increase the level of safety when drilling wells. It was shown that the developed methods and models could be used to simulate and identify a wide class of complications on drilling rigs functioning under conditions of an a priori and current uncertainty about their structure, parameters, and geo-environment