COMPARATOR REGRESSION ANALYSIS IN CONDITIONS OF FUZZY INITIAL DATA

Abstract

Abstract. The canonical task of regression analysis consists in studying the problem of estimation and mathematical description of the influence caused by one or more independent variables (predictors, explanatory variables) on the dependent (explained) variable. The subject of comparator identification problem is a specific modification of the standard regression analysis problem in the case when, for some reason, it is not possible to measure values of the dependent, explained variable. However, the problem of reconstructing a regression polynomial can be solved if it is possible to qualitatively compare the results of experiments and rank them, for example, in the order of increasing. Taking into account the results of ranking the values of the explained variable in different experiments, a corresponding system of inequalities is formed. The purpose of the research consists in developing a method for mathematical processing of the resulting system of inequalities for analytical assessment of the level of influence of explanatory variables on the explained variable. The method for solving the problem is based on transforming a system of inequalities into a system of linear algebraic equations. A significant drawback of the known approach to solving this problem consists in the fact that the resulting system of linear algebraic equations is an underdetermined one (the number of unknowns in this system exceeds the number of equations). At the same time, the system has an infinite number of solutions, among which there may be an uncontrollable number of unacceptable ones. The exhaustive search method for finding acceptable solutions is futile. In this regard, the problem of developing a correct method of comparator identification remains relevant. Another difficulty that accompanies the actual procedure of comparator identification when solving practical problems consists in the fact that measurements of values of the controlled parameters are not accurate. The uncertainty that arises in the conditions of a small sample of initial data can be removed using the tools of fuzzy mathematics. It is assumed that, based on preliminary research, a mathematical description of the corresponding membership function can be obtained for each of the controlled parameters. As a result, effective approaches to solving emerging problems have been proposed, based on the use of developed optimization procedures in the conditions of a small sample of fuzzy initial data.

Keywords

• comparator identification
• underdetermined system of equations
• fuzziness of initial data
• small sample
• fuzzy optimization