6.  P-Innovative and P-Pseudo-Innovative Systems on the Predicate P and Their Properties

In this chapter we shall continue to study the concept of efficiency, and in line with this concept we introduce the definition of an innovative smart system. After that in terms of algebraic formalization we shall describe the structure of innovative smart systems. Then we shall consider the concept of pseudo-innovation system, dual to the concept of an innovative smart system. Also an algebraic formalization of some properties of innovative smart systems and pseudo-innovative systems is constructed. Some examples of the use of these concepts consumed in the expert systems in training, and in the economy are given. After that we shall continue the empirical study of the process of system’s decomposition using the example of the decomposition of the education system on the basis of these questions. The algorithm for a comprehensive assessment of the effectiveness of the functioning of the innovation system based on the tensor estimation of system performance is also proposed in this chapter. It is proposed to use homomorphisms of the group G _s of factors defining the system S into the group GL(n,∆) of linear homogeneous transformations of the vector space R ⁿ as tensor estimates of the efficiency of the functioning of the system S. One can also consider homomorphisms of the group of factors G _s that define a system S in the group GL (n,∆) of linear homogeneous transformations of the vector space ∆n over an arbitrary field ∆.