Quantitative estimation of fuzzy crisis management

Abstract

The model and the description of the numerical assessment of uncertain (fuzzy) controls in the implementation of the crisis management in the so-called "gray area", combining transient states of the system, is presented in the article. The behavior of the economic (financial) system is described by a multidimensional vector, for example, the Altman five-factor model. The estimates given by this model are distributed over three ranges, corresponding to the stable state of the system, the negative state, and the "gray area" in which the trajectory of movement towards the bankruptcy zone is outlined and consisting of the states which can be evaluated by means of fuzzy variables, characterizing proximity to the bankruptcy zone. According to the values of these state variables, controls must be implemented to bring the system into a stable favorable zone. The general apparatus for determining crisis management strategies is sufficiently developed, at the same time, the determination of the numerical characteristics of these controls, as an independent task, requires further formalization and development of numerical methods. This article contains one possible formalization  and its implementation using the analytical library of the Python language. The presented model and algorithm are quite universal and can be relatively simply adapted taking into account the specific features of the problem. A distinctive feature of the approach proposed in the article, for example in comparison with neural network models, is a decrease in the degree of subjectivity in the choice of the control rules. This degree is determined here not by the function of the corresponding fuzzy measure, but by the weight coefficients of the significance of crisis management options and the real resources for their implementation.