The first chapter of the thesis analyses the problem and components of social security. A literature review was conducted and it was found that the level of well-being of the population is one of the key components of social security.
The second section of the thesis analyses the mathematical tool for assessing the level of security. The second section of the thesis consists of five subsections. The first subsection describes in detail the basic concepts of fuzzy set theory. Since Matlab software is used for mathematical modelling in this thesis, the second subsection of the thesis discusses the basic membership functions available in the Fuzzy Logic Designer (FLD) application of Matlab software. This subsection provides both a graphical representation and an analytical view of the corresponding membership functions.
In the third subsection of the second chapter of the thesis, the basic operations on fuzzy sets are considered. For greater clarity, the corresponding operations on fuzzy sets are also presented in a graphical representation.
In the fourth subsection of the second chapter of the thesis, the main stages of fuzzy inference are considered. In the case of the defuzzification stage, the relevant defuzzification methods are presented both in graphical and analytical form.
In the fifth subsection of the second chapter of the thesis, the main algorithms of fuzzy inference are considered. For greater clarity, the stages of FIS for each of the considered algorithms are also presented in graphical form.
The third chapter of the dissertation consists of four subsections. Each subsection describes in detail the method and algorithm for constructing fuzzy inferenceto determine the level of the relevant aspect of the population's well-being.
The first subsection of the third section describes in detail the algorithm for building the FIS-tree structure to determine the level of economic well-being of the population of Ukraine in comparison with the member countries of the Organisation for Economic Co-operation and Development (OECD). The constructed FIS-tree consists of 4 fuzzy inference systems (FIS), namely, Income (net household wealth and per capita income), Housing (number of rooms per person, housing costs and housing with basic facilities) and Job (employment and long-term unemployment). The output of these FIS serves as input for the next FIS, the Economic Indicators, which provides the level of economic well-being of the Ukrainian population in comparison with OECD countries.
The second subsection of the third section describes in detail the algorithm for building the structure of the FIS-tree to determine the level of social well-being of the population of Ukraine in comparison with the member countries of the OECD. The constructed FIS-tree consists of 9 FIS, namely the FIS Education (level of education of the population, students' skills and expected duration of study), the FIS Health (life expectancy, self-reported health - the percentage of people who rated their health as “good” or “very good”), the FIS Security (homiciderate and feeling safewalkingaloneatnight). The next FIS (Community, Civicengagement, and Life Satisfaction) have a simpler structure than those discussed earlier. These FIS consist of one input indicator, respectively: quality of supportnetwork, voterturnout, life satisfaction. In this subsection, the following grouping of the above indicators is proposed: FIS Basic needs for living (consisting of the FIS Education, Health and Security) and the FIS Public and social relations(consisting of the FIS community, civicengagement and life satisfaction). The output of these FIS serves as input for the next FIS, Social Indicators, which provides the level of social well-being of the Ukrainian population in comparison with OECD countries.
The third subsection of the third chapter describes the algorithm for building a FIS that assesses Ukraine's environmental well-being in comparison with OECD countries. In the future, this FIS will also be an element of the FIS-tree, and will serve as an input parameter for the last FIS considered in this study.
In the fourth subsection of the third chapter, the structure of the FIS-tree is built, which consists of all the above-mentioned FIS and contains a new FIS that assesses the well-being of the Ukrainian population in comparison with OECD countries. In total, the built model consists of 15 FIS and 307 fuzzy logic rules. The output of the model is the level of well-being of the population of Ukraine in comparison with the OECD member countries.
