MATHEMATICAL MODELING OF THE TASK OF DETERMINING A SET OF CONTROL EVENTS USING A FUZZY METHOD OF ANALYSIS OF HIERARCHIES AND A METHOD BASED ON MEASURING LATENT VARIABLES
N.E. Krasova, N.A. Aleynikova
The article discusses the mathematical modeling of the problem of multi-criteria selection of control measures for the ongoing monitoring of performance using two methods: a method of fuzzy analysis of hierarchies and a method based on measuring latent variables (the Rush method). Both methods are expert methods. The advantage of using a fuzzy hierarchy analysis method is to describe the relative attribute values using fuzzy numbers instead of exact ones. Due to this, the expert gets the opportunity not only to assess the degree of preference of one object over another, but also to express his doubts, experience, intuition in this assessment. The main disadvantage of this approach is the complexity and complexity of the calculations. The advantages of the Rush method are in the simplicity of calculations, in the transition from the subjective assessments of experts to the objective ones, which possess the property of linearity. Within the framework of the constructed hierarchical model aimed at increasing the efficiency of the learning process, weights of different types of control measures are determined by these methods. In the future, the weights obtained can be used as parameters in the models for the formation of a set of control measures based on minimizing the difficulty of their implementation and maximizing their usefulness.
Keywords: expert estimation methods, pairwise comparison matrix, fuzzy analysis of hierarchies, latent variables, Rush method.