Comparator identification in the conditions of bifuzzy initial data

Abstract

When solving a large number of problems in the study of complex systems, it becomes necessary to establish a relationship between a variable that sets the level of efficiency of the system's functioning and a set of other variables that determine the state of the system or the conditions of its operation. To solve this problem, the methods of regression analysis are traditionally used, the application of which in many real situations turns out to be impossible due to the lack of the possibility of direct measurement of the explained variable. However, if the totality of the results of the experiments performed can be ranked, for example, in descending order, thus forming a system of inequalities, the problem can be presented in such a way as to determine the coefficients of the regression equation in accordance with the following requirement. It is necessary that the results of calculating the explained variable using the resulting regression equation satisfy the formed system of inequalities. This task is called the comparator identification task.

The paper proposes a method for solving the problem of comparator identification in conditions of fuzzy initial data. A mathematical model is introduced to describe the membership functions of fuzzy parameters of the problem based on functions (L–R) – type. The problem is reduced to a system of linear algebraic equations with fuzzy variables.

The analytical relationships required for the formation of a quality criterion for solving the problem of comparator identification in conditions of fuzzy initial data are obtained. As a result, a criterion for the effectiveness of the solution is proposed, based on the calculation of membership functions of the results of experiments, and the transformation of the problem to a standard problem of linear programming is shown. The desired result is achieved by solving a quadratic mathematical programming problem with a linear constraint. The proposed method is generalized to the case when the fuzzy initial data are given bifuzzy