Sustainable Development Gauging Matrix Mathematical Model

We characterize sustainable development by two main constituents: security of population (Isec) and quality of their life (Iql), as “Figure 1”. Then the generalized sustainable development measure (Index) may be presented by a quaternary {Q} with imaginary scalar part j(Isec), describing security of people and real vector part (Iql), describing quality of life in the space with three dimensions: economic (Iec), ecological (Ie) and social-institutional (Is):

In this space for each country we have the sustainable development radius-vector (Isd) with the Euclidean norm:

 

which we define as a sustainable development index (Isd).  Quality of life component (Iql) is the sustainable development vector (Isd) projection on the ideal vector with coordinates (1; 1; 1). 

The angle (α) is defined as a degree of harmonization:

Since simulation of security and quality of life is carried out using different methods and different initial data it seems reasonable to fulfill it separately in three stages. At the first stage we will carry out Data Analysis of Quality of Life Component of Sustainability. In order to perform this simulation we have to select of data by means of which each of three sustainable development dimensions can be presented most adequately. These data are also to be prepared by reputable international organizations or research centers annually on the permanent basis.

To present economic dimension two global data bases were used: - Global Competitiveness Index (Іc), annually developed by the World Economic Forum (The Global Competitiveness Report, 2007-2008), and Index of economic freedom (Ief) developed by Heritage Foundation (The news of intellectual centre of Heritage Foundation, 2008).

Ecological dimension (Iе) is defined by the well-known Environmental Performance Index, which is annually formed by the Center on environmental legislation and policy of Yele University together with Columbia University (EPI Beta, 2007/2008).

Social dimension is formed by three global indices:- Quality of life Index, developed by the International Living organization (Quality of Life Index, 2008), Human development index, annually calculated in the framework of United Nations Development Program (Human Development Report, 2007/2008) and Index of knowledge society, created by UN Department on economic and social development (The publications of the United Nations on economic and social affairs – UNDESA, 2005). All together these six indices are defined by 12 policy categories and 65 indicators and accumulated at the Ukrainian branch of World Data Center (WDC for Geoinformatics and Sustainable Development, 2008).

Based on the description of interconnections between these factors, their transformation to the unified computational platform, the mathematical model for Quality of Life Simulation, named “Sustainable Development Gauging Matrix” (SDGM) was developed as “Figure 3”.

This interdisciplinary model is a large scale matrix compression. It combines data of various natures and reflects the balance between three inseparable spheres of the society – economic, ecological and social/institutional. Under such conditions all data, indicators and indices, which are included in the SDGM model, are measured in different units and have various interpretations. This is why they are reduced to the normal form in such a way that their changes and the changes of their indices themselves were in the range from 0 to 1. In this case the lowest values of the above indicators will correspond to the numerical values close to 0, and the highest – will approximate these values to 1. Such normalization allows one to calculate each of the indices Iec, Ie, Is and Isd in the form of an algebraical compression of its constituents with the corresponding weighted coefficients. In turn, the weighted coefficients in the calculation formula of the sustainable development index (Isd) are chosen in such a way that allows one to provide the same weights of economic, ecological and social measures in this index.