Development of technological knowledge made possible to elaborate the mathematical theory of technology. Its starting point is an exact, however, informal definition of technology as a system of knowledge. Basing on this definition, two classes of technologies (the general and specific technologies) are introduced to reflect the situation existing in industry and engineering. This provides for the construction of a general mathematical model of a specific technology as well as for the development of a relevant mathematical apparatus and exact methods for an investigation and design of various technologies (in industry, management, information processing and so on). The crucial point of this new theory of technology is a mathematical model of a technology based on a concept of a technological operator acting on the space of worked materials. A technology (according to this model) is either a separate technological operator or a system of technological operators that are organized by a special coordinating technological operator. Each technological operator describes some stage of a technological process in a complete form.
The mathematical theory of technology utilizes new mathematical disciplines such as theory of named sets, fuzzy set theory, and theory of structured multidimensional models of systems and processes as well as traditional fields such as algebra, theory of probabilities, and theory of algorithms.
In the mathematical theory of technology such problems as reliability,
equivalence, stability, constructibility, and realizability of technologies
are studied. The aim is the development of efficient methods and algorithms
of the computer aided design of technologies