Self-employment in the Russian Federation is a special tax regime; tax on personal income is a simplified form of entrepreneurship. The self-employed are often associated with freelancers. The exponential growth of information increases uncertainty, and the development of digitalization levels out uncertainty. This work analyses the factors influencing the digitalization development of self-employment as an integral indicator that can affect the sustainability of self-employment. The main method used is a topological method based on the polymerase chain reaction method, as well as the model based on fuzzy sets theory – Mamdani fuzzy inference algorithms. The data for the study were collected through a survey posted on Google Forms. The respondents were experts in the self-employment sector. Eight people participated in the survey (4 – self-employed; 4 – university professors). The self-employed comprised the following areas: developer – 1; service worker – 1; online marketer – 1; musician, event host – 1. Further calculations were performed in Mathlab. According to the study results, the level of factors in the development of self-employed digitalization is 0.502, which corresponds to the third interval of the five-level classifier and has growth potential.

The idea behind the creation of the GDP matrix is to obtain innovative products and opportunity matrices, which will be formed by chains of sectors of the economy using the following algorithm. The most innovatively developed sectors of the economy are located at the edges of the GDP matrix according to the queue (for example, 1-3-5-7-8-6-4-2). In such a scheme, innovatively less developed sectors of the economy, located in the middle of the GDP matrix, have the most contacts, which give them the opportunity to gain more skills and abilities. The most distal sectors of the matrix have fewer contacts, but in view of greater economic development, they will generate the innovative ideas and be the last link forming or receiving the end-product. Each newly formed opportunity matrix (GDP') can serve as a template for the creation of new innovative ideas and products.

The arsenal of methods available to economics can be enriched by examining its problems from different points of view and using technologies developed from complex natural systems. In this study, using the example of the creation of opportunity matriсes, we describe a method for chain innovative transformation of economic processes using an intersectoral GDP matrix directly analogous to the DNA matrix in the polymerase chain reaction that revolutionized molecular biology. The idea behind the creation of the GDP matrix is to obtain innovative products and opportunity matrices, which will be formed by chains of sectors of the economy using the following algorithm. The most innovatively developed sectors of the economy are located at the edges of the GDP matrix according to the queue (for example, 1-3-5-7-8-6-4-2). In such a scheme, innovatively less developed sectors of the economy, located in the middle of the GDP matrix, have the most contacts, which give them the opportunity to gain more skills and abilities. The most distal sectors of the matrix have fewer contacts, but in view of greater economic development, they will generate the innovative ideas and be the last link forming or receiving the end-product. Each newly formed opportunity matrix (GDP') can serve as a template for the creation of new innovative ideas and products. Using the proposed approach, the economic miracles of Singapore, South Korea, and Hong Kong are considered along with the prospect of innovative development for African countries that have not yet undergone industrialization.