The main purpose of this paper is to show some conceptual fundamentals for a new theory of mathematical interpretation TMI, which can be used for solving the non-formalised and heavy-formalised tasks in different areas of science. This theory has all principal factors, which are inherent to any theory. Foremost, this theory has the historical, theoretical, mathematical and simulation fundamentals. In addition, it has the mathematical description as a set of the postulates. Thus, this theory will be able to expand a sphere of using of an existing mathematical tool in other specific areas of science and some possibilities for their further application. This everything is confirming the uniformity and comprehensiveness of the existing mathematical tool, and it is showing some possibilities of a mutual penetration of different areas to each other.
['Sergii Kavun']
Conceptual fundamentals of a theory of mathematical interpretation