Hierarchy

For other uses, seeHierarchy (disambiguation).

"Subordinate" redirects here. For other uses, seeSubordination.

The mediaevalscala naturaeas a staircase, implying thepossibility of progress:Ramon Llull'sLadder of Ascent and Descent of the Mind,1305

Ahierarchy(fromGreek:ἱεραρχία,hierarkhia,'rule of a high priest', fromhierarkhes,'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such asarchitecture,philosophy,design,mathematics,computer science,organizational theory,systems theory,systematic biology,and thesocial sciences(especiallypolitical science).

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'ssubordinates,although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following apath.All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to twoco-workersorcolleagues;each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy.Heterarchyis one such form.

Nomenclature

See also:Glossary of graph theory,Taxonomy (general),andStructure

Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (seebelow).

In an organizational context, the following terms are often used related to hierarchies:

• Object:one entity (e.g., a person, department orconceptor 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
  • Rank:the relativevalue,worth,complexity,power,importance,authority,level etc. of an object
  • Levelor 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 aninverted-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)
    • adirectinteraction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on atree,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 apathfrom one object to another
  • Span:aqualitativedescription 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 (ingraph theory), thegeneral terminologyused is different.

Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, withdata structures,objects are known asnodes,superiors are calledparentsand subordinates are calledchildren.In a business setting, a superior is asupervisor/ Bossand a peer is acolleague.

Degree of branching

Degreeofbranchingrefers to the number of directsubordinatesor children an object has (in graph theory, equivalent to the number of otherverticesconnected 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:linearandbranching.

In alinear hierarchy,the maximum degree is 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 theobjectsand not thelevels;every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects.

In abranching hierarchy,one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher).For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy.Branching hierarchies are present within numerous systems, includingorganizationsandclassification schemes.The broad category of branching hierarchies can be further subdivided based on the degree.

Aflat hierarchy(also known for companies asflat organization) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span.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,diamondsandgraphiteare flat hierarchies of numerouscarbonatoms that can be further decomposed into subatomic particles.

Anoverlapping hierarchyis a branching hierarchy in which at least one object has two parent objects.For example, agraduate studentcan have twoco-supervisorsto whom the student reports directly and equally, and who have the same level of authority within theuniversityhierarchy (i.e., they have the samepositionortenurestatus).

Etymology

Possibly the first use of the English wordhierarchycited by theOxford English Dictionarywas in 1881, when it was used in reference to the three orders of three angels as depicted byPseudo-Dionysius the Areopagite(5th–6th centuries). Pseudo-Dionysius used the relatedGreekword (ἱεραρχία,hierarchia) both in reference to thecelestial hierarchyand theecclesiastical hierarchy.The Greek termhierarchiameans 'rule of a high priest',fromhierarches(ἱεράρχης, 'president of sacred rites, high-priest')and that fromhiereus(ἱερεύς, 'priest')andarche(ἀρχή, 'first place or power, rule').Dionysius is credited with first use of it as an abstract noun.

Since hierarchical churches, such as theRoman Catholic(seeCatholic Church hierarchy) andEastern Orthodoxchurches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally withGodas the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods insecularsettings.

Representing hierarchies

Maslow's hierarchy of human needs.This is an example of a hierarchy visualized with a triangle diagram. The hierarchical aspect represented here is that needs at lower levels of the pyramid are considered more basic and must be fulfilled before higher ones are met.

A hierarchy is typically depicted as apyramid,where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole.For example, the fewDirectorsof a company could be at theapex,and thebasecould be thousands of people who have no subordinates.

These pyramids are oftendiagrammedwith atrianglediagram which serves to emphasize the size differences between the levels (but not all triangle/pyramid diagrams are hierarchical; for example, the 1992USDA food guide pyramid). An example of a triangle diagram appears to the right.

Another common representation of a hierarchical scheme is as atree diagram.Phylogenetic trees,chartsshowing the structure of§ Organizations,andplayoff bracketsin sports are often illustrated this way.

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 includefractalmaps,TreeMapsandRadial 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 ofvisual 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 aVenn 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 asetin which:

1. No element is superior to itself, and
2. One element, the (apexorhierarch), is superior to all of the other elements in the set.

The first requirement is also interpreted to mean that a hierarchy can have nocircular relationships;the association between two objects is alwaystransitive. The second requirement asserts that a hierarchy must have a leader orrootthat is common to all of the objects.

Mathematical representation

Main article:Hierarchy (mathematics)

Mathematically, in its most general form, a hierarchy is apartially ordered setorposet.Thesystemin 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 resultinglevelsis referred to as aclass.

"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

Matryoshka dolls,also known asnesting dollsorRussian dolls.Each doll is encompassed inside another until the smallest one is reached. This is the concept ofnesting.When the concept is applied tosets,the resulting ordering is anested hierarchy.

A nested hierarchy orinclusion hierarchyis a hierarchical ordering ofnested sets.The concept of nesting is exemplified in Russianmatryoshka 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:

${\text{square}}\subset {\text{quadrilateral}}\subset {\text{polygon}}\subset {\text{shape}}\,$

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 canonlybe a quadrilateral; it can never be atriangle,hexagon,etc.

Nested hierarchies are the organizational schemes behindtaxonomiesand systematic classifications. For example, using the originalLinnaean taxonomy(the version he laid out in the 10th edition ofSystema Naturae), a human can be formulated as:

${\text{H. sapiens}}\subset {\text{Homo}}\subset {\text{Primates}}\subset {\text{Mammalia}}\subset {\text{Animalia}}$

Taxonomies may change frequently (as seen inbiological taxonomy), but the underlying concept of nested hierarchies is always the same.

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 ofself-similarityandrecursion.Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.

Containment hierarchy

A diagram illustrating a containment hierarchy. The set of all squares is completely contained in the larger set of quadrilaterals, and so on.

A containment hierarchy is a direct extrapolation of thenested hierarchyconcept. All of the ordered sets are still nested, but every set must be "strict"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

${\text{square}}\subsetneq {\text{quadrilateral}}\subsetneq {\text{polygon}}\subsetneq {\text{shape}}\,$

The notation$x\subsetneq y\,$meansxis a subset ofybut is not equal toy.

A general example of a containment hierarchy is demonstrated inclass inheritanceinobject-oriented programming.

Two types of containment hierarchies are thesubsumptivecontainment hierarchy and thecompositionalcontainment hierarchy. A subsumptive hierarchy "subsumes"its children, and a compositional hierarchy is"composed"of its children. A hierarchy can also be both subsumptiveandcompositional.

Subsumptive containment hierarchy

Asubsumptivecontainment 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-Ahierarchy ".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 levelMammalia"is a" member of the levelAnimalia;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".For example, with the Linnaean hierarchy outlined above, an entity name likeAnimaliais a way to group all the species that fit theconceptualizationof an animal.

Compositional containment hierarchy

Acompositionalcontainment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.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 thehierarchy of life.Every person can be reduced toorgan systems,which are composed oforgans,which are composed oftissues,which are composed ofcells,which are composed ofmolecules,which are composed ofatoms.In fact, the last two levels apply to allmatter,at least at themacroscopic scale.Moreover, each of these levels inherit all the properties of theirchildren.

In this particular example, there are alsoemergent properties—functions that are not seen at the lower level (e.g.,cognitionis not a property ofneuronsbut is of thebrain)—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. Theselevel hierarchiesare characterized by bi-directionalcausation.Upward causationinvolves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children.Downward causationrefers to the effect that the incorporation of entityxinto a higher-level entity can have onx's properties and interactions. Furthermore, the entities found at each level areautonomous.

Contexts and applications

Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically.Some conventional definitions of the terms "nation"and "government"suggest that everynationhas a government and that every government is hierarchical. Sociologists can analyse socioeconomic systems in terms of stratification into a social hierarchy (thesocial stratificationof societies), and allsystematic classification schemes(taxonomies) are hierarchical.Mostorganized religions,regardless of their internal governance structures, operate as a hierarchy underdeitiesandpriesthoods.ManyChristian denominationshave anautocephalousecclesiastical hierarchyofleadership.Families can be viewed as hierarchical structures in terms ofcousinship(e.g., first cousin once removed, second cousin, etc.),ancestry(as depicted in afamily tree) andinheritance(successionandheirship). All the requisites of a well-rounded life andlifestylecan be organized usingMaslow's hierarchy of human needs- according to Maslow's hierarchy of human needs.Learningsteps often follow a hierarchical scheme—to masterdifferential equationsone must first learncalculus;to learn calculus one must first learnelementary algebra;and so on.Natureoffers hierarchical structures, as numerous schemes such asLinnaean taxonomy,theorganization of life,andbiomass pyramidsattempt to document.

While the above examples are oftenclearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, mostpostal-codesystems are hierarchical. Using theCanadian postal code systemas an example, the top level's binding concept, the"postal district",consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of anoverlapping hierarchy,because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the formatA0A 0A0(the second and third letter positions allow 20 objects each). Mostlibrary classificationsystems are also hierarchical. TheDewey Decimal Systemis infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.

A simple militaryorganizational hierarchydepicted in the form of atree.Diagrams like this exemplifyorganizational charts.

Organizations

Main articles:Organizational structureandHierarchical organization

Organizationscan be structured as adominance hierarchy.In an organizational hierarchy, there is a single person or group with the mostpowerorauthority,and each subsequent level represents a lesser authority. Most organizations are structured in this manner,includinggovernments,companies,armed forces,militiaandorganized religions.The units or persons within an organization may be depicted hierarchically in anorganizational chart.

In areverse hierarchy,the conceptualpyramidof 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

Main article:Biological organisation § Fundamentals

Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure.On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity.Systemhierarchies analysis performed in the 1950s,laid the empirical foundations for afieldthat would become, from the 1980s,hierarchical ecology.

The theoretical foundations are summarized bythermodynamics. Whenbiological systemsare modeled asphysical systems,in the most general abstraction, they arethermodynamic open systemsthat exhibitself-organisedbehavior, and theset/subsetrelations betweendissipative structurescan be characterizedin a hierarchy.

Other hierarchical representations related to biology includeecological pyramidswhich illustrate energy flow ortrophic levelsinecosystems,andtaxonomichierarchies, including theLinnean classificationscheme andphylogenetic treesthat reflect inferred patterns of evolutionary relationship among living and extinct species.

Computer-graphic imaging

Main article:3D modeling

CGIandcomputer-animationprogramsmostly use hierarchies for models. On a3Dmodel of ahumanfor example, thechestis aparentof the upper left arm, which is a parent of the lower left arm, which is a parent of thehand.This pattern is used inmodelingandanimationfor almost everything built as a 3Ddigitalmodel.

Linguistics

Many grammatical theories, such asphrase-structure grammar,involve hierarchy.

Direct–inverse languagessuch asCreeandMapudungundistinguish subject and object onverbsnot by different subject and object markers, but via a hierarchy of persons.

In this system, the three (or four withAlgonquian languages) persons occur in a hierarchy ofsalience.To distinguish which is subject and which object,inverse markersare 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 byHeinrich Schenker(1768–1835, seeSchenkerian analysis), and in the (1985)Generative Theory of Tonal Music,by composerFred Lerdahland linguist RayJackendoff). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background orUrsatz,which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature.

Thepitchesandformoftonalmusic are organized hierarchically, all pitches deriving their importance from their relationship to atonickey, and secondary themes in otherkeysare brought back to the tonic in a recapitulation of the primary theme.

Examples of other applications

Information-based

• Library classification
  • Dewey Decimal Classification

City planning-based

• Green transport hierarchy
• Roads
  • Streets
• Settlement hierarchy
  • As of 2010
  • As of 2100 (estimate according to Doxiadis, 1968)

Linguistics-oriented

• Language family tree
• Levels of adequacy for evaluating grammars
• Direct–inverse languages
• Structural linguistics
  • Parse tree
  • Formal grammars
  • Abstract syntax tree
• Evolution of basic color terminology in languages

Power- or authority-based

• Aristocratic hierarchies
  • InEurope
  • InChina
• Ecclesiastical hierarchies
  • Catholic Church hierarchy
  • LDS Church hierarchy
  • Kimbanguist Church hierarchy
  • Raëlism Church hierarchy
  • see alsoautocephaly
• Prussian three-class franchise
• Political party hierarchies
  • Nazi Party(paceoverlapping fields)
    • SS
    • Hierarchy of subdivisions within the Gau
  • Communist Party of the Soviet Union
  • Chinese Communist Party
• Chain of command
  • Military ranks
  • Military units
  • U.S. Military Combatant Commands
• Intraspecial dominance
  • Pecking order
• Social classes
  • Caste system in India
  • Hierarchical structure of Feudal Japan
  • White racist hierarchy
  • Hierarchy of Exclusion(Ender's Game)

Value-related

• Hierarchy of genres in art
• Evidence
• Human needs
• Precious substances
• Judicial hierarchy of social values

Perception-based

• Color wheel
  • Primary colors
    • Secondary colors
      • Tertiary colors

History-oriented

• Three-age system
• Cyclic theory of civilization
  • Oswald Spengler
  • Arnold J. Toynbee
• Spiral dynamics

Science-focussed

• Hierarchy of organization within the Universe
• Star systems
• Biological classification
• Biological organization
• Phylogenetic tree
• Evolutionary development
• Hierarchy of ecological georegions

Technology-based

• Memory hierarchy
  • Cache hierarchy
• Clusters
• Class constructs
• Data organization
  • Hierarchical query
• Data storage
  • Computer files
• Devices
• IP addresses
• Memory
  • Virtual memory allocation
• Networks
• Radio cells
• States (configurations)
• Web addresses
• Structure
  • Data Structure
• Inheritance (object-oriented programming)

Religion-related

• Levels of consciousness
  • Chakras
  • Great chain of being
  • G.I. Gurdjieff
  • Timothy Leary
• Levels of spiritual development
  • InTheravada Buddhism
  • InMahayana Buddhism
• Ages in the evolution of society
  • InAstrology
  • InHellenism (the Ancient Greek Religion)
  • Dispensations in Protestantism
  • Dispensations in Mormonism
• Degrees of communion between various Christian churches
• UFO religions
  • Command hierarchy of theAshtar Galactic Commandflying saucer fleet
• Deities
  • InJapanese Buddhism
  • InTheosophy
• Angels
  • InChristianity
  • InIslam
  • InJudaism
    • Kabbalistic
  • InZoroastrianism
• Devils and Demons
  • Devils
  • Demons
• Hells
  • InCatholicism (Nine Levels of Hell)
  • InBuddhism (Sixteen Levels of Hell)
• 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 clustering of networks
• 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 asWilliam James(1842 to 1910),Michel Foucault(1926 to 1984) andHayden White(1928 to 2018), important critiques of hierarchicalepistemologyare advanced. James famously asserts in his workRadical Empiricismthat clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved.

Feminists,Marxists,anarchists,communists,critical theoristsand others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc.

Ethics, behavioral psychology, philosophies of identity

Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.

Inethics,variousvirtuesare enumerated and sometimes organized hierarchically according to certain brands ofvirtue theory.

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 statePages displaying short descriptions of redirect targets
• 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 rulesPages displaying wikidata descriptions as a fallback
• Hierarchical epistemology– A theory of knowledge
• Hierarchical hidden Markov model
• Hierarchical INTegration– computer benchmarkPages displaying wikidata descriptions as a fallback
• Hierarchical organization– Type of organizational structure
• Hierarchical Music Specification Language– Music programming language
• Hierarchy Open Service Interface Definition– programmatic interface specifications describing servicesPages displaying wikidata descriptions as a fallback
• Hierarchy problem– Unsolved problem in physics
• Holarchy § Different meanings
• Instrumental value– Philosophical conceptPages displaying short descriptions of redirect targets
• 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 authoritiesPages displaying short descriptions of redirect targets
  • Characters of Halo § High Prophets
  • List of Coptic Orthodox Popes of Alexandria
• Peter Principle– Management concept by Laurence J. PeterPages displaying short descriptions of redirect targets
• Ring (computer security)– Layer of protection in computer systemsPages displaying short descriptions of redirect targets
• Social dominance theory– Theory of intergroup relations

Structure-related concepts

(For example, in§ Subtypes)

• Is-a
  • Hypernymy(andsupertype)
  • Hyponymy(andsubtype)
• Has-a
  • Holonymy
  • Meronymy

Footnotes

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,Bibcode:1956Sci...123.1127E,doi:10.1126/science.123.3208.1127,PMID17793430
• Jordan, F.; Jørgensen, S. E. (2012),Models of the Ecological Hierarchy: From Molecules to the Ecosphere,Newnes,ISBN9780444593962
• Margalef, R. (1975), "External factors and ecosystem stability",Schweizerische Zeitschrift für Hydrologie,37(1): 102–117,Bibcode:1975AqSci..37..102M,doi:10.1007/BF02505181,hdl:10261/337692,S2CID20521602
• O'Neill, R. V. (1986),A Hierarchical Concept of Ecosystems,Princeton University Press,ISBN0691084378
• Wicken, J. S.; Ulanowicz, R. E. (1988), "On quantifying hierarchical connections in ecology",Journal of Social and Biological Systems,11(3): 369–377,doi:10.1016/0140-1750(88)90066-8

Further reading

• Ahl, Valerie;Allen, Timothy F. H.(1996).Hierarchy Theory.New York: Columbia University Press.ISBN0-231-08481-1.
• Akl, Selim G.;Taylor, Peter D. (1983).Cryptographic solution to a multilevel security problem(PDF).Advances in Cryptology – Proceedings ofCRYPTO'82. New York:Plenum Publishing Corporation.pp. 237–249.ISBN0-306-41366-3.Archived fromthe 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.hdl:1807/118234.ISBN978-0-494-27682-2.
• 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.ISBN978-3-540-72688-3.
• Nelson, Julie(1992). "Gender, Metaphor and the Definition of Economics".Economics and Philosophy.8(1): 103–25.doi:10.1017/S026626710000050X.S2CID146493891.
• Pumain, Denise (2006).Hierarchy in Natural and Social Sciences.New York, New York:Springer-Verlag.ISBN978-1-4020-4126-6.
• 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.hdl:1807/119833.ISBN978-0-494-28076-8.
  • 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).Carnegie Mellon University,Pittsburgh, Pennsylvania:International Society for Bayesian Analysis:221–228.arXiv:math/0510449.Bibcode:2005math.....10449S.doi:10.1214/07-ba209.ISSN1936-0975.S2CID10611032.Archived fromthe original(PDF)on 2015-09-03.
  • Shahbaba, Babak; Neal, Radford M. (2006)."Gene function classification using Bayesian models with hierarchy-based priors".BMC Bioinformatics.7.London, England:BioMed Central:448.arXiv:q-bio/0605015.Bibcode:2006q.bio.....5015S.doi:10.1186/1471-2105-7-448.ISSN1471-2105.PMC1618412.PMID17038174.

External links

• Media related toHierarchyat 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)