METHODICAL APPROACHES TO CONSTRUCTION OF FUNCTIONS OF FUZZY MATHEMATICAL MODELS

Abstract

The paper generalizes scientific and methodological approaches to the development of economic and mathematical models based on the theory of fuzzy logic and linguistic variable. Forecasting and decision support using fuzzy mathematical models allows to summarize and concentrate expert information, to predict the course of processes in various fields, taking into account quantitative and qualitative factors. In comparison with known expert methods, the theory of fuzzy logic has a number of advantages, the main of which are the automation of calculations through the use of mathematical packages, such as Matlab, Scilab; the ability to learn models, use quantitative and qualitative properties of the object of modeling, obtain solutions for various related problems on the basis of one knowledge base filled with expert, analytical and experimental information, and others. It is substantiated that the construction of membership functions is one of the main stages in the construction of fuzzy mathematical models. The main ways in which you can build membership functions depending on the method of obtaining information are considered. Two methods are used to construct membership functions: the involvement of many experts and the involvement of one expert. The method of constructing membership functions involves fassification of fuzzy estimates of influencing factors. The phase of fasification involves the choice of fuzzy terms for the linguistic assessment of the influencing factors given on the corresponding universal sets. The most common membership functions are generalized, which include triangular, trapezoidal, Gaussian, sigmoid. An example of an expert questionnaire is given, which should be used when building a mathematical model based on information from a group of experts. An example of constructing membership functions for a conditional linguistic variable is given. Calculating the eigenvector of a matrix of pairwise comparisons significantly increases the complexity of using a mathematical model. Therefore, we propose to use consistent pairwise comparisons. Despite the fact that in mathematical packages the construction of membership functions is automated, the primary choice of form and characteristics should be carried out by calculation methods considered in the work.