Algebraic Formalization of Smart Systems by Natalia Serdyukova & Vladimir Serdyukov

Author:Natalia Serdyukova & Vladimir Serdyukov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.New status of a system Q, on which system S affects.

3.New status as a result of an external agency of a system S upon outdoor environment U,

So, we have the target vectors and a final status of a system S, corresponding to the vector , in which the system S moved as a result of it’s functioning. The following cases are possible:

(a) 2 3, (b) 3 2, (c) 3 1, (d) 1 3.

The graph the impact of targets of a system S upon the environment U runs as follows:

Now based on the introduced notations and concepts one can go to the formalization of an axiomatic description of the purposes and principles of the system approach. Generally adopted axiomatic (even verbal one) of the system approach or of the theory of systems does not exist.

Usually the following main principles are chose while describing the system: the presence of a target (set of targets), integrity (wholeness), hierarchy, good structure. Basic system’s principles are opened in the following way. Integrity means fundamental irreducibility properties back to the sum of the properties of its constituent elements and revivalist of the last properties of the whole, the dependence of each element, properties and relationships of the system from his place, functions, etc. within the whole. Good structure means the ability to describe the system through the establishment of its structure, i.e., network connections and relations of the system, the dependence of the system behavior from the behavior of its individual elements and the properties of its structure, the interdependence of the system and environment. Hierarchy means that each component of the system can be considered as a system and the analyzed system represents one component of a broader system in this case. The adequate knowledge of the system requires building many different models, each of which describes some aspect of the system because of the principal complexity of each system. Let’s describe main system’s principles using narrow predicate calculus. This runs as follows.

The principle of integrity is set to items 1 and 2:1.

system S possesses all the properties and there exists at least one property P, such that no one of own subsystems of the system S does not possessed P. Thus, the property of integrity allocates system as one having a synergistic effect (at least one).

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