Models of Using Qualitative Values of Statistical Indicators in Organizational Management Systems

Abstract

One of the tasks involved in the decision-making process of the governing bodies of organizational management systems is to analyze information from management objects and other sources. This information tends to be of a statistical nature and contains quantitative estimates of certain indicators. The number of such estimates can reach several thousand values, which makes it difficult or even impossible to use them directly in the decision-making process. This is due to the fact that decision makers (DM), as confirmed in psychology, can effectively operate with only a small number of indicator values. Therefore, there is a need to replace the quantitative values of the parameters with their qualitative characteristics. To solve this problem, the paper uses linguistic variables that map quantitative values of indicators to verbally described qualitative values. The paper substantiates the approach of choosing the type of membership functions of fuzzy sets corresponding to qualitative values of statistical indicators and choosing a reasonable number of qualitative values, which is illustrated by an example of crime situation assessment. The complexity of the problem of using qualitative values of the indicators is determined by the presence of the factor of partial uncertainty arising from the lack of clear boundaries between the values; mathematically it is described as “linkage” of the support of the membership functions of the above fuzzy sets. This leads to the need to use vector estimates of the indicators, where each qualitative value is compared with a quantitative measure of the possibility of occurrence of this value. The paper describes a method for predicting qualitative values of statistical indicators using vector estimations, which is illustrated by solving the problem of predicting changes in the crime situation in different situations of changes in the factors affecting it.