International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.


The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.


HIERARCHY (General) 2)

Prof. M. KALAIDJIEVA (Institute of Control and Systems Research of Sofia, Bulgaria) proposed the following postulates for a general concept of hierarchy. She writes:


1. A general hierarchie GH is an one-dimensionally orientated multi-dimensional structure of constructs (structures), up to infinite dimensional.

2. Each general hierarchie is represented by two coupled GHs – one GH with an inverse general hierarchie having exactly the same structure, but defined with the opposite orientation of its direction.

3. Deadlocks are tolerable within a GH, only if they can be represented as cycles interruptible at a defined place under defined conditions.

4. A theoretical contextual difference is made between elements and nodes of a hierarchie. Many methods of modeling GHs rely on this seperation.

5. The nodes of a GH may have both multiple outgoing and in-going connections. This particular feature is polyhierarchie. A general hierarchie having the feature of polyhierarchie is called polyhierarchie GH or shortly – polyhierarchie.

6. A general hierarchie need not be connected in all its parts. The mutual belonging of several parts possess individual identic or similar contextual characteristics, stating that number of (dis)connected structures are (parts of) one and the same general hierarchie.

7. The contextual characteristic is called invariant characteristic (IC). The contextual ICs are described (defined) in natural language; their variety is unrestricted. There are nine primary ICs: direction, aspect of decomposition, element, node, connection, (algorithm of, rules of decomposition, polihierarchie, polythematics, measure. They might be independent of one another or not depending on the context of GH design and analysis. Four secondary ICs are derived from the system of the primary nine composition, inverse hierarchie, level and step.

8. General hierarchy (ies) may be modified (rearranged) by

a) Operations wich build by construction set up an algebra in the special mathematical sense of this term. They are addition, subtraction multiplication and division. Basic elements of the algebra are of two kinds of bases:

- 1 order base of algebra containing constructs of 2 nodes bound with 1 connection (or 2 connections bound with 1 node);

- 2 order base of the algebra containing constructs of 1 nodes, all its subnodes and bound with as many connections.

b) Altering the values or meanings of invariant characteristic(s). Such changes may also change the degree of abstractness of modeling complex objects in GH(s) or change the context of modelled constructs, e.g. for comaparative study.

c) Special operations typical only for the set of general hierarchies and bound to the context of the GH(s): normalize GH(s) on one and the same level, haul up and haul down across level (steps).


  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented


Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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