Hierarchical structures (Figure 1.10, b, c, c, g)...

Hierarchical structures (Figure 1.10, b, c, c, g)

They represent the decomposition of the system in space. All components (vertices, nodes) and links (arcs,

node connections) exist in these structures simultaneously (not spaced in time). Such structures can have not two (as for simplicity is shown in Figures 1.10, b and c), but a greater number of levels of decomposition (structuring). Structures in which each element of the lower level is subordinated to one node (one vertex) of the superior (and this is true for all levels of the hierarchy) is called tree structures of type "tree", structures on which the tree order relation is performed, hierarchical structures with strong strong links (see Figure 1.10, b).

Fig. 1.10

Structures in which the lower-level element can be subordinated to two or more nodes (vertices) of the superior is called hierarchical structures with " weak connections (see Figure 1.10, in ).

The hierarchical structures shown in Fig. 1.10, b and in, correspond to the matrix structures in Fig. 1.10, r and b. Relationships that look like weak connections between the two levels in Fig. 1.10, c, are similar to the ratios in the matrix formed from the components of these two levels in Fig. 1.10, b. And the + in Fig. 1.10, d means there is a connection between the elements of the system in Fig. 1.10, c, and the - the absence of such communication.

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, goals and functions (see Chapter 5), the production and organizational structures of enterprises (see Chapter 8) are most widespread.

Hierarchies with weak relationships are used in cases where goals are formulated too close to ideal aspirations and not enough funds for their implementation, to represent some types of organizational structures (see, for example, linear functional structures in Chapter 8, vertical links in the governance structure of the state in rice 1.18).

In general, the term hierarchy (from Greek ιεραρχία) is broader, it means "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 characterize the relationship 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 principle 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 relationships. 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 [72] considers the following types of hierarchies: dominant (similar to an inverted tree with a base at the top); hollarchy (dominant hierarchies with feedback) and Chinese box, or modular hierarchies. The latter grow in size from the simplest components (internal boxes) to all larger aggregates (external boxes). In biology, there are hierarchies in which the new upper levels appear sequentially in the evolutionary process.

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