Approximation to the Theory of Affinities to Manage the Problems of the Grouping Process

Anna M. Gil-Lafuente, Anna Klimova

Perhaps more than ever, new economic and enterprise needs have increased the interest and utility of the methods of the grouping process based on the theory of uncertainty. Numerous studies made in this field until recently have contributed with a great number of techniques and algorithms that proved their efficiency in resolving challenging problems that arise in an economic management framework of modern companies. A fuzzy grouping (clustering) process is a key phase of knowledge acquisition and reduction complexity regarding different groups of objects. In this study, we consider some elements of the theory of affinities and uncertain pretopology which form a significant support tool for a fuzzy clustering process. A Galois lattice is also introduced in order to provide a clearer vision of the results we obtained in a previous process. We implement this useful set of mathematical elements to make an homogeneous grouping process of the economic regions of Russian Federation and Ukraine. The obtained results give us a large situational panorama of a regional economic situation of two countries as well as the key guidelines to follow in a decision-making process. We offer the calculus for two different countries to demonstrate the significant differences that could be obtained taking into account the minimum changes of an input data basis. The mathematical method is very sensible to any changes that the economic situation of the regions can have. In this study, we pretend to give an alternative method of the grouping process for any modern company that performs its activity under uncertainty.