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The study provides solutions for the scientific task related to the improvement of theoretical and development of methodological and applied principles, and the identification and evaluation of risks and threats as factors of anti-crisis management of the enterprises. Based on the developed concept of quantitative risk analysis, we constructed a fuzzy hierarchical model, which gives the possibility to get the estimates: risk factors; specific types of threats in the framework of a process; risk processes, identified in the anti-crisis management; and the integrative risk of anti-crisis management. Furthermore, the proposed model makes it possible to identify the threats that are the risks of the highest (catastrophe) layer. The fuzzy hierarchical model construction process includes the determination of linguistic variables, term-varieties, and universal sets for quantitative evaluation of figures and risks, the establishment of parameters of the membership functions for indicators and risks, the formation of fuzzy knowledge bases, the construction of a fuzzy hierarchical model in the MATLAB environment, the evaluation of adequacy of model based on the learning sample, the correction of a model, and the adoption of a resolution regarding its final variant. The use of the model in the anti-crisis enterprise management will provide the anti-crisis team with the possibility to give early warning of all negative factors, give their quantitative evaluation, and take them into account in the course of making managerial decisions. [ABSTRACT FROM AUTHOR]