# Structure - Theory of Information Processes and Systems

## Structure

The system can be represented by a simple enumeration of elements or a black box (model "input-exit"). However, most often when researching an object this representation is not enough, as it is required to find out what the object is, what it accomplishes the set goal, and obtain the required results. In these cases, the system is mapped by subdivision into subsystems, components, elements with interrelations that can have a different character, and introduce the concept of structure.

The structure (from the Latin structure, meaning structure, location, order) reflects certain relationships, the arrangement of the components of the system, its structure, structure .

In complex systems, the structure does not include all elements and connections, between them (in the extreme case, when the concept of structure is applied to simple, completely deterministic objects, the concepts of structure and system coincide), but only the most essential components and connections that are small Change under the current functioning of the system and ensure the existence of the system and its basic properties. In other words, the structure characterizes the organization of the system, the stable ordering of elements and connections.

Structural connections have relative independence from elements and can act as an invariant in the transition from one system to another, transferring the patterns revealed and reflected in the structure of one of them to others. In this case, the systems can have a different physical nature.

The same system can be represented by different structures depending on the stage of cognition of objects or processes, from the aspect of their consideration, the purpose of creation. However, as the research progresses or during the design process, the structure of the system may change.

Structures, especially hierarchical ones, can help in uncovering the uncertainty of complex systems. In other words, structural representations of systems are a means of their investigation. In this regard, it is useful to identify certain types and forms of representation of structures.

Structural representations can be a means of researching systems. Different types of structures have specific features and can be regarded as independent concepts of system theory and system analysis. Briefly describe the main of them (Figure 3.3).

Fig. 3.3. Types of system structures

Typically, the concept of structure associated with a graphical display. However, this is not necessary. The structure can be represented in matrix form, in the form of set-theoretic descriptions, using the language of topology, algebra, and other systems modeling tools.

The network structure , or network (Figure 3.3, a), represents the decomposition of the system in time.

Such structures can display the order of the operation of the technical system (telephone, electrical network, etc.), the stages of human activity (in the production of products - network diagram, in the design - network model, in planning - network plan, etc.). ).

In the form of network models in the following chapters are presented the methods of system analysis.

When using network models, use a certain terminology: vertex, edge, path, critical path , etc. Elements of the network can be located in series and in parallel.

Networks are different. The most common and convenient for analysis are unidirectional networks. But there can be networks with feedbacks and cycles. For the analysis of complex networks, there is a mathematical apparatus of graph theory, an applied theory of network planning and management, widely used in the presentation of processes of organization of production and enterprise management.

Hierarchical structures (Figure 3.3, bd) represent the decomposition of the system in space. All components (vertices, nodes) and links (arcs, knot connections) exist in these structures simultaneously (not spaced in time). Such structures can have not two (as for simplicity is shown in Figures 3.3, b and c), but a greater number of levels of decomposition (structuring). The structures shown in Fig. 3.3, b, in which each element of the lower level is subordinate to one node (one vertex) of the superior (and this is true for all levels of the hierarchy), are called tree structures of type " ; tree ", structures in which the tree order or hierarchical structures with strong links.

The structures shown in Fig. 3.3, in, in which the lower-level element can be subordinated to two or more nodes (vertices) of the superior, are called hierarchical structures with "weak" connections.

The hierarchical structures shown in Fig. 3.3, b and in, correspond to the matrix structures of Fig. 3.3, е, ж. Relationships that have the form of "weak" connections between the two levels in Fig. 3.3, c, are similar to the ratios in the matrix formed from the components of these two levels in Fig. 3.3, x.

Tree-like hierarchical structures with the help of which they represent the constructions of complex technical products and complexes, the structure of classifiers and dictionaries, the goals and functions of management systems and information systems of enterprises and organizations are most widespread.

Hierarchies with weak links are used in cases where goals are formulated too close to ideal aspirations and not enough resources for their implementation, for the presentation of some types of organizational structures (for example, in linear-functional structures).

In general, the term hierarchy (from the Greek ιεραρχία - the sacred and the power) was originally used in a broader sense, as "subordination, the order of subordination of inferior in rank and rank of persons higher, arose as the name of the service ladder in religion" ; is widely used to describe relationships in the apparatus of government, the army, etc., then the concept of hierarchy was extended to any order of objects agreed upon by subordination.

Therefore, in hierarchical structures it is only important to single out the levels of subordination, and between the levels and between components within a level, in principle, there can be any relationship. In accordance with this, there are structures that use the hierarchical principle, but which have specific features, and they should be distinguished especially.

In particular, T. Saati considers the following types of hierarchies: dominant (similar to an inverted tree with a stem at the top), hollarchy (dominant hierarchies with feedback), and a Chinese box or modular hierarchies. The latter grow in size from the simplest components (inner boxes) to larger collections (outer boxes). In biology, there are hierarchies in which the new upper levels arise sequentially in the evolutionary process.

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