Model of an Economic and Social Decision Support Tool Using Algebraic Properties of Families of Solutions of Fuzzy Relational Systems of Inequalities

The COVID-19 pandemic has forced many countries to introduce deeply economically intrusive restrictions. The consequences of these decisions are difficult to predict. The aim of this article is to present the mathematical basis of a decision support system based on the study of relationships between data sets. For example, we can analyze the relationship between the degree of closure of individual industries and the number of bankruptcies of companies in these industries. Fuzzy relational systems of equations and inequalities were used to model the system.  This method allows us to examine the minimum and maximum degree of dependence between the decisions made and their consequences to better adjust them. Work on relational systems was introduced for medical applications by Ellie Sanchez as early as 1976, and new applications and properties are still being explored. In order, to effectively study the relationships between different, usually large, data sets using mathematical apparatus, the MoFRI system is being developed. It will allow for the simulation of the impact of individual changes on various areas of the economy.