An asymmetric vertical order in a system through which elements or subsystems of a lower level of complexity are regulated or controlled by one or several others of successively higher level.
The hierarchy model itself, as an isomorphism, generally pervades any specific hierarchized system, i.e. the subsystems themselves, down from level to level, are true to the hierarchical type.
M.D. MESAROVIC, D. MACKO and Y. TAKAHARA developed a general "Theory of Hierarchical, Multilevel Systems" (1970) in which they study the concept of hierarchy, the basic types of hierarchies, the levels of complexity and establish a mathematical theory of coordination in unconstrained or constrained systems. As stated by these authors: "The requirements for proper functioning of a system on any stratum appear as conditions of constraints on the operation on the lower strata" and"… for a proper functioning of the system on a given stratum, all the lower strata have to function correctly" (p.41).
According to J.C. LUGAN a cybernetic hierarchy of systems can be established wherein information rich systems tend to control energy rich ones (1993, p.46).
According to J. A. GOGUEN and F.J. VARELA: "The idea of hierarchy is often presented from the point of view of the interdependence of different levels of systems descriptions. Particular instances of hierarchical structures including multilevel cooperation can be found. GOGUEN presents a general theory of hierarchical systems of interdependent processes. Its basic ideas are interconnection, behavior and level, and its theoretical framework is categorical algebra" (1979, p.35).
The most obvious function of hierarchies is the coordination one, which is quite visible in living systems. However, in human organizations this role can be obscured when coordination is managed by ill-informed and authoritarian controllers. Another important function for the higher strata in hierarchies is adaptation and creativity in case of important changes in the environment.
From the basic viewpoint of the nature of hierarchy, and according to D. BOHM and F.D. PEAT it is a result of "… the activity of the generative principle within the generative order" (1987, p.164).
According to this view, hierarchy results of the progressive morphogenesis of complexity. Remains to be seen how this generative order, which seems to be at work in all complex systems, organizes morphogenesis.
A complex system generally shows various hierarchic levels, the lower ones being embedded into the higher ones. A. KOESTLER emphasized the "double-faced" aspect of elements in a hierarchy: they function as wholes in relation to lower levels and as elements of wholes at a higher level.
A good example of hierarchy is found in any complex living system, as shown by J. G. MILLER (1978).
The concept of hierarchy implies asymmetric dependence relations. It is in this sense that, as stated by D. WILSON, the taxonomic Linnean hierarchy is "… a system of nested classes whose members are individual organisms" (1969, p.4).
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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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