Hierarchy
A hierarchy (from
A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's
Nomenclature
Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below).
In an organizational context, the following terms are often used related to hierarchies:[1][2]
- Object: one entity (e.g., a person, department or concept or element of arrangement or member of a set)
- System: the entire set of objects that are being arranged hierarchically (e.g., an administration)
- Dimension: another word for "system" from on-line analytical processing (e.g. cubes)
- Member: an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension)
- Terms about Positioning
- power, importance, authority, level etc. of an object
- Level or Tier: a set of objects with the same rank OR importance
- Ordering: the arrangement of the (ranks or levels)
- Hierarchy: the arrangement of a particular set of members into (ranks or levels). Multiple hierarchies are possible per (dimension taxonomy or Classification-system), in which selected levels of the dimension are omitted to flatten the structure
- Terms about Placement
- Hierarch, the apex of the hierarchy, consisting of one single orphan (object or member) in the top level of a dimension. The root of an inverted-tree structure
- Member, a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached
- Orphan, a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level
- Leaf, a member in any level of a dimension without subordinates in the hierarchy
- Neighbour: a member adjacent to another member in the same (level or rank). Always a peer.
- Superior: a higher level or an object ranked at a higher level (A parent or an ancestor)
- Subordinate: a lower level or an object ranked at a lower level (A child or a descendant)
- Collection: all of the objects at one level (i.e. Peers)
- Peer: an object with the same rank (and therefore at the same level)
- Interaction: the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
- a direct interaction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on a tree, the two objects have a line between them)
- Distance: the minimum number of connections between two objects, i.e., one less than the number of objects that need to be "crossed" to trace a path from one object to another
- qualitativedescription of the width of a level when diagrammed, i.e., the number of subordinates an object has
- Terms about Nature
- Attribute: a heritable characteristic of (members and their subordinates) in a level (e.g. hair-colour)
- Attribute-value: the specific value of a heritable characteristic (e.g. Auburn)
In a mathematical context (in graph theory), the general terminology used is different.
Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with
Degree of branching
Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: linear and branching.
In a linear hierarchy, the maximum degree is 1.[1] In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. This is referring to the objects and not the levels; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects.
In a branching hierarchy, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher).
A flat hierarchy (also known for companies as flat organization) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span.[2] Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles.
An overlapping hierarchy is a branching hierarchy in which at least one object has two parent objects.
Etymology
Possibly the first use of the English word hierarchy cited by the Oxford English Dictionary was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, hierarchia) both in reference to the celestial hierarchy and the ecclesiastical hierarchy.[3] The Greek term hierarchia means 'rule of a high priest',[4] from hierarches (ἱεράρχης, 'president of sacred rites, high-priest')[5] and that from hiereus (ἱερεύς, 'priest')[6] and arche (ἀρχή, 'first place or power, rule').[7] Dionysius is credited with first use of it as an abstract noun.
Since hierarchical churches, such as the
Representing hierarchies
A hierarchy is typically depicted as a
could be thousands of people who have no subordinates.These pyramids are often
Another common representation of a hierarchical scheme is as a
More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees.
Visual hierarchy
In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of visual hierarchy. Visual hierarchy is also important for proper organization of files on computers.
An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information. The child element is within the parent element, such as in a Venn diagram. This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located.
For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. Child elements are towards the bottom of the stairs and parent elements are at the top. This structure represents hierarchical relationships through the use of visual stacking.
Informal representation
In plain English, a hierarchy can be thought of as a set in which:[1]
- No element is superior to itself, and
- One element, the (apex or hierarch), is superior to all of the other elements in the set.
The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive. The second requirement asserts that a hierarchy must have a leader or
Mathematical representation
Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.[9] The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.
"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.
Subtypes
Nested hierarchy
A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets.[10] The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:
A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be a quadrilateral; it can never be a triangle, hexagon, etc.
Nested hierarchies are the organizational schemes behind
Taxonomies may change frequently (as seen in
In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.[12]
Containment hierarchy
A containment hierarchy is a direct extrapolation of the
The notation means x is a subset of y but is not equal to y.
A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming.
Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy "
Subsumptive containment hierarchy
A subsumptive containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "IS-A hierarchy".[9][14][15] The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is a member of the level Mammalia "is a" member of the level Animalia; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "concepts".[15] For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal.
Compositional containment hierarchy
A compositional containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.[16] Most engineered structures, whether natural or artificial, can be broken down in this manner.
The compositional hierarchy that every person encounters at every moment is the
In this particular example, there are also
Contexts and applications
Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically.
While the above examples are often[
Organizations
In a reverse hierarchy, the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings.
Biology
Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure.[25] On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity.[26] System hierarchies analysis performed in the 1950s,[27][28] laid the empirical foundations for a field that would become, from the 1980s, hierarchical ecology.[29][30][31][32][33]
The theoretical foundations are summarized by thermodynamics. When
Other hierarchical representations related to biology include
Computer-graphic imaging
Linguistics
Many grammatical theories, such as
In this system, the three (or four with Algonquian languages) persons occur in a hierarchy of salience. To distinguish which is subject and which object, inverse markers are used if the object outranks the subject.
On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways.
Music
The structure of a musical composition is often understood hierarchically (for example by
The pitches and form of tonal music are organized hierarchically, all pitches deriving their importance from their relationship to a tonic key, and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme.
Examples of other applications
Information-based |
City planning-based
|
Linguistics-oriented
|
Power- or authority-based
|
|
Perception-based
|
History-oriented
|
Science-focussed
|
Technology-based
|
- Levels of consciousness
- Chakras
- Great chain of being
- G.I. Gurdjieff
- Timothy Leary
- Levels of spiritual development
- In Theravada Buddhism
- In Mahayana Buddhism
- In
- Ages in the evolution of society
- In Astrology
- In Hellenism (the Ancient Greek Religion)
- Dispensations in Protestantism
- Dispensations in Mormonism
- Degrees of communion between various Christian churches
- UFO religions
- Deities
- In Japanese Buddhism
- In Theosophy
- Angels
- In Christianity
- In Islam
- In Judaism
- Kabbalistic
- In Zoroastrianism
- In
- Devils and Demons
- Devils
- Demons
- Hells
- Religions in society
- (organizational hierarchies are listed under "Power- or authority-based")
Methods using hierarchy
- Analytic Hierarchy Process
- Hierarchical Decision Process
- Hierarchic Object-Oriented Design
- Hierarchical Bayes model
- Hierarchical clustering
- Hierarchical constraint satisfaction
- Hierarchical linear modeling
- Hierarchical modulation
- Hierarchical proportion
- Hierarchical radial basis function
- Hierarchical storage management
- Hierarchical task network
- Hierarchical temporal memory
- Hierarchical token bucket
- Hierarchical visitor pattern
- Presentation-abstraction-control
- Hierarchical-Model-View-Controller
Criticisms
In the work of diverse theorists such as
Ethics, behavioral psychology, philosophies of identity
In
In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason.
See also
- Anarchy – Society without authorities or a governing body, against religion
- Class browser – Feature of coding platforms
- Forms of government– System or group of people governing an organized community, often a state
- Graph theory – Area of discrete mathematics
- Heterarchy – System of organization where the elements of the organization are unranked
- Hierarchical classifier– classification system based on hierarchical rules
- Hierarchical epistemology – A theory of knowledge
- Hierarchical hidden Markov model
- Hierarchical INTegration – computer benchmark
- Hierarchical Music Specification Language – Music programming language
- Hierarchy Open Service Interface Definition– programmatic interface specifications describing services
- Hierarchy problem – Unsolved problem in physics
- Holarchy § Different meanings
- Instrumental value– Philosophical concept
- Layer (disambiguation)
- Multilevel model – Statistical models of parameters that vary at more than one level
- Multitree – Directed acyclic graph with ≤1 directed paths between any two nodes
- Ordinary (officer)– Ecclesiastical title for local authorities
- Characters of Halo § High Prophets
- List of Coptic Orthodox Popes of Alexandria
- Peter Principle– Management concept by Laurence J. Peter
- Ring (computer security)– Layer of protection in computer systems
- Social dominance theory – Theory of intergroup relations
(For example, in § Subtypes)
Footnotes
- ^ ISBN 0-521-29086-4.
- ^ JSTOR 985254.(registration required)
- ^ "Catholic Encyclopedia: Hierarchy". Archived from the original on 2021-01-26. Retrieved 2005-04-27.
- ^ "hierarchy". Online Etymology Dictionary. Archived from the original on 2018-07-04.
- ^ Henry George Liddell; Robert Scott. "ἱεράρχης". A Greek–English Lexicon. Archived from the original on 2021-07-03 – via Perseus Digital Library.
- ^ Henry George Liddell; Robert Scott. "ἱερεύς". A Greek–English Lexicon. Archived from the original on 2020-09-28 – via Perseus Digital Library.
- ^ Henry George Liddell; Robert Scott. "ἀρχή". A Greek–English Lexicon. Archived from the original on 2011-06-06 – via Perseus Digital Library.
- ^ Douglas Lemke (2002). Regions of War and Peace. Cambridge: University of Cambridge. p. 49.
- ^ ISBN 3-540-61534-2.
- ^ ISBN 978-1-4020-4126-6.
- ISBN 0-665-53008-0. Archivedfrom the original on 2008-10-10. Retrieved 2011-09-24.
- ISBN 978-0691145471.
- ISSN 0302-9743.
- ^ "Compositional hierarchy". WebSphere Transformation Extender Design Studio. Archived from the original on 3 January 2013. Retrieved 9 October 2009.
- ^ ISBN 978-0-8493-0607-5.
- ISBN 0-8264-5428-3.
- ISBN 1-4020-0757-4.
- ISBN 978-0-19-861022-9. Archived from the originalon 2007-09-29. Retrieved 2009-10-08.
- ISBN 978-0-19-861022-9. Archived from the originalon 2007-09-29. Retrieved 2009-10-08.
- ^ "Social Stratification | Overview, Theories & Examples - Video & Lesson Transcript". study.com. Archived from the original on 2022-06-24. Retrieved 2022-06-24.
- ^
ISBN 9780521212878. Retrieved 26 November 2021.
- ^
Kulish, Viktor Vasylevych (11 April 2006) [2002]. Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics. Volume 123 of Fundamental Theories of Physics. Vol. 1. New York: Springer Science & Business Media (published 2006). p. xviii. ISBN 9780306480614. Retrieved 26 November 2021.
At the same time, it is a trivial phenomenon of everyday life, too. Indeed, one can be convinced that there is a hierarchy in everyday life everywhere. We can affirm once more that a person lives in a completely hierarchical world.
- ^ Walker, Randy (May–June 2009). "Tracking Nuclear Sources" (PDF). wellservicingmagazine.com. pp. 28–30.[permanent dead link]
- ^ "Organizational Chart and Hierarchy: Definition & Examples - Video & Lesson Transcript". study.com. Archived from the original on 2022-06-24. Retrieved 2022-06-24.
- from the original on 2022-06-24. Retrieved 2022-06-24.
- ^ "Artificial Intelligence - foundations of computational agents -- 2 Agent Architectures and Hierarchical Control". artint.info. Archived from the original on 2022-07-04. Retrieved 2022-06-24.
- ^ Evans 1951
- ^ Evans 1956
- ^ Margalef 1975
- ^ O'Neill 1986
- ^ Wicken & Ulanowicz 1988
- ^ Pumain 2006
- ^ Jordan & Jørgensen 2012
- ^
ISBN 9780826449108. Retrieved 26 November 2021.
Kühne believes the Prussian franchise lasted for over sixty years because it accurately reflected the social realities of the relatively closed, hierarchical, and conformist communities of rural Prussia.
- ^
Compare:
Lee, Stephen J. (12 February 2016) [1987]. "Dictatorship in Germany". European Dictatorships 1918-1945 (4, revised ed.). London: Routledge (published 2016). p. 217. ISBN 9781317294221. Retrieved 26 November 2021.
[...] Nazi administration is now regarded as an overlapping and confusing 'polycracy'. The basis of the criticism is that the multi-layering of agencies and the lack of proper delineation between them generated conflict and hampered efficiency. There was, for example, extensive rivalry between the Four-Year plan Office, the Ministry of Economics, the War ministry and the Plenipotentiary for Economics.
Works cited
- Evans, F. C. (1951), "Ecology and urban areal research", Scientific Monthly (73)
- Evans, F. C. (1956), "Ecosystem as basic unit in ecology", Science, 123 (3208): 1127–8, PMID 17793430
- Jordan, F.; Jørgensen, S. E. (2012), Models of the Ecological Hierarchy: From Molecules to the Ecosphere, Newnes, ISBN 9780444593962
- Margalef, R. (1975), "External factors and ecosystem stability", Schweizerische Zeitschrift für Hydrologie, 37 (1): 102–117, S2CID 20521602
- O'Neill, R. V. (1986), A Hierarchical Concept of Ecosystems, Princeton University Press, ISBN 0691084378
- Wicken, J. S.; Ulanowicz, R. E. (1988), "On quantifying hierarchical connections in ecology", Journal of Social and Biological Systems, 11 (3): 369–377,
Further reading
- Ahl, Valerie; ISBN 0-231-08481-1.
- ISBN 0-306-41366-3. Archived from the original(PDF) on 2002-12-29.
- Carbone, June; Cahn, Naomi (2013). "Is marriage for rich men?". Nevada Law Journal. 13 (2). William S. Boyd School of Law: 6.
- Ckurshumova, Wenzislava (2007). Regulatory hierarchies in auxin signal transduction and vascular tissue development (PhD thesis). University of Toronto. Section B. ISBN 978-0-494-27682-2.
- Galindo, Cipriano; Fernández-Madrigal, Juan-Antonio (2007). Kacprzyk, Janusz (ed.). Multiple Abstraction Hierarchies for Mobile Robot Operation in Large Environments. Studies in Computational Intelligence. Berlin: Springer Berlin Heidelberg. ISBN 978-3-540-72688-3.
- S2CID 146493891.
- Pumain, Denise (2006). Hierarchy in Natural and Social Sciences. New York, New York: ISBN 978-1-4020-4126-6.
- Rosenbaum, A. (2000). Les représentations hiérarchiques en philosophie (in French). Paris: Desclee de Brouwer.
- Shahbaba, Babak (2007). Improving classification models when a class hierarchy is available (PhD thesis). University of Toronto. Section B. ISBN 978-0-494-28076-8.
- Also includes full copies of:
- Shahbaba, Babak; Neal, Radford M. (2007). "Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior" (PDF). Bayesian Analysis. 2 (1). S2CID 10611032. Archived from the original(PDF) on 2015-09-03.
- Shahbaba, Babak; Neal, Radford M. (2006). "Gene function classification using Bayesian models with hierarchy-based priors". PMID 17038174.
External links
- Media related to Hierarchy at Wikimedia Commons
- Principles and annotated bibliography of hierarchy theory (archived 7 February 2002)
- Summary of the Principles of Hierarchy Theory — S.N. Salthe (archived 21 July 2006)