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| | == Nike Air Jordan Damen 'Nach meiner Lieferung == |
| A '''hierarchy''' (Greek: hierarchia (ἱεραρχία), from [[hierarch]]es, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another.
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| Abstractly, a hierarchy can be [[Mathematical model|modelled mathematically]] as a [[rooted tree]]: the root of the tree forms the top level, and the children of a given vertex are at the same level, below their common parent. However, a rooted tree does not allow for items to be "at the same level as" one another, since a tree prohibits cycles. To accommodate this, a hierarchy can be modeled using a [[graph (mathematics)|graph]] or a [[preorder|pre-order relation]] on the set of items. Alternatively, items of like type can be grouped together, and the hierarchy can be modeled using a [[partial order|partial order relation]] on the set of sets-of-like-items.
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| A hierarchy (sometimes abbreviated HR) can link entities either directly or indirectly, and either vertically or horizontally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Indirect hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a [[path (graph theory)|path]]. All parts of the hierarchy which 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 two [[co-worker]]s or [[colleague]]s; 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. [[Heterarchy]] (sometimes abbreviated HT) is one such form.
| | == Louis Vuitton Taschen Midlife markiert den Punkt == |
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| ==Nomenclature==
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| {{see also|Glossary of graph theory}}
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| Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see [[#Visualization|below]]).
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| | </ul> |
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| The generic hierarchy uses the following terms:<ref name="Dawkins"/><ref name="Architecture"/>
| | == Ralph Lauren Pullover und die Bösen == |
| * '''[[Entity|Object]]''': one entity (e.g., a person, department or [[concept]]) or element of arrangement or member of a set
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| * '''[[System]]''': the entire set of objects that are being arranged hierarchically (e.g., an administration)
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| * '''[[Dimension]]''': another word for "system" from on-line analytical processing (e.g. cubes)
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| * '''[[Element (mathematics)|Member]]''': an (element or object) in a (system or dimension) at any (level or rank)
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| * '''[[Ranking|Rank]]''': the relative [[value (ethics)|value]], worth, [[complexity]], [[Power (philosophy)|power]], [[importance]], [[authority]], level etc. of an object
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| * '''[[wikt:level#Noun|Level]]''': a set of objects with the same rank OR importance
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| * '''[[Order of precedence|Ordering]]''': the arrangement of the (ranks or levels)
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| * '''Hierarchy''': the arrangement of a particular set of (ranks or levels) i.e. multiple hierarchies are possible per (dimension or system)
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| * '''[[Family of sets|Collection]]''': all of the objects at one level
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| * '''[[Superior (hierarchy)|Superior]]''': a higher level or an object ranked at a higher level (parent or ancestor)
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| * '''[[wikt:Subordinate|Subordinate]]''': a lower level or an object ranked at a lower level (child or descendent)
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| * '''[[wikt:Hierarch|Hierarch]]''', the top level of the hierarchy, usually consisting of one object or member of a dimension
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| * '''[[wikt:Peer|Peer]]''': an object with the same rank (and therefore at the same level)
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| * '''[[wikt:neighbour|Neighbour]]''': the adjacent level/ranking (the immediate superior and immediate inferior)
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| * '''[[Interpersonal relationship|Interaction]]''': the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
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| ** 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 (graph theory)|tree]], the two objects have a line between them)
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| * '''[[Distance (graph theory)|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 (graph theory)|path]] from one object to another
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| * '''[[wikt:Span|Span]]''': a [[qualitative data|qualitative]] description of the width of a level when diagrammed, i.e., the number of subordinates an object has
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| (N.B., while hierarchies are commonly studied using [[graph theory]], the general terminology used is different, and words such as "direct" may have different general meanings)
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| Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with [[data structure]]s, objects are known as [[node (computer science)|nodes]], superiors are called [[parent node|parents]] and subordinates are called [[child node|children]]. In a business setting, a superior is a [[supervisor|supervisor/boss]] and a peer is a [[colleague]].
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| ===Degree of branching===
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| [[Degree (graph theory)|Degree]] of [[branch (graph theory)|branching]] refers to the number of direct [[#Terminology|subordinates]] or children an object has (equivalent to the number of [[vertex (graph theory)|vertices]] 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''.
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| In a '''linear hierarchy'''<!--per WP:R#PLA, this SHOULD be bold-->, the maximum degree is 1.<ref name="Dawkins"/> In other words, all of the objects can be visualized in a lineup, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that 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. An example of a linear hierarchy is the [[hierarchy of life]].
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| In a ''''''branching hierarchy''''''<!--per WP:R#PLA, this SHOULD be bold-->, one or more objects has a degree of 2 or more (and therefore the maximum degree is 2 or higher).<ref name="Dawkins"/> For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy.<ref name="Dawkins"/> Branching hierarchies are present within numerous systems, including [[organization]]s and [[classification scheme]]s. The broad category of branching hierarchies can be further subdivided based on the degree.
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| A ''''''flat hierarchy''''''<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which the maximum degree approaches infinity, i.e., with a wide span.<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proceedings of the American Philosophical Society]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania}}</ref> 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 at first blush. For example, [[diamond]]s and [[graphite]] is a flat hierarchy of numerous [[carbon]] atoms which can be further decomposed into subatomic particles.
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| An ''''''overlapping hierarchy''''''<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which at least one object has two parent objects.<ref name="Dawkins"/> For example, a [[graduate student]] can have two [[research supervisor|co-supervisors]] to whom the student reports directly and equally, and who have the same level of authority within the [[university]] hierarchy (i.e., they have the same [[list of academic ranks|position]] or [[tenure]] status.
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| ==History of the term==
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| Possibly the first use of the English word "hierarchy" cited by the [[Oxford English Dictionary]] was in 1880, 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 language|Greek]] word (''hierarchia'') both in reference to the [[De Coelesti Hierarchia|celestial hierarchy]] and the [[ecclesiastical hierarchy]].<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> The Greek term "ἱεραρχία" means "rule by priests" (from "ἱεράρχης" – ''ierarches'', meaning "president of sacred rites, high-priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28era%2Frxhs ἱεράρχης],
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| Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref> and that from "ἱερεύς" – ''iereus'', "priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs ἱερεύς], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref> + "ἀρχή" – ''arche'', amongst others "first place or power, rule"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F ἀρχή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>), and Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the [[Roman Catholicism|Roman Catholic]] (see [[Catholic Church hierarchy]]) and [[Eastern Orthodoxy|Eastern Orthodox]] churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with [[God in Christianity|God]] as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in [[secular]] settings.
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| ==Visualization==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
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| [[File:Maslow's hierarchy of needs.png|thumb|right|200px|[[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. This is an example of a hierarchy visualized with a triangle diagram.]]
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| A hierarchy is typically depicted as a [[pyramid (geometry)|pyramid]], 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 few [[Board of Directors|Directors]] of a company could be at the [[apex (geometry)|apex]], and the [[Base (geometry)|base]] could be thousands of people who have no subordinates.
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| These pyramids are typically diagrammed with a [[tree structure|tree]] or [[triangle]] [[diagram]] (but note that not all triangle/pyramid diagrams are hierarchical), both of which serve to emphasize the size differences between the levels. An example of a triangle diagram appears to the right. An [[organizational chart]] is the diagram of a hierarchy within an [[organization]], and is depicted in tree form [[#Organizations|below]].
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| 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 space map|fractal maps]], [[treemapping|TreeMaps]] and [[Radial tree|Radial Trees]].
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| ==Visual hierarchy==
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| 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.
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| An example of visually representing hierarchy is through the Nest structure. The Nest structure represents hierarchical relationships by using layers of information. The child element is within the parent element, such as in a Venn diagram. This structure of representing hierarchy is most effective in representing simple 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.
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| 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. The child elements are towards the bottom of the stairs and the parent elements are at the top. This structure is effective when representing more complicated hierarchies where steps are not placed in obvious sequences. Further steps are concealed unless all of the steps are revealed in sequence. In the computer desktop example, a file that is being sought after can only be found once another file is opened. The link for the desired file is within another document. All the steps must be completed until the final destination is reached.
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| ==Informal representation==
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| In plain English, a hierarchy can be thought of as a [[Set (mathematics)|set]] in which:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|authorlink=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|booktitle=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editors=Bateson, Paul Patrick Gordon; Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>
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| # No element is superior to itself, and
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| # One element, the ''hierarch'', is superior to all of the other elements in the set.
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| The first requirement is also interpreted to mean that a hierarchy can have no [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]].
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| The second requirement asserts that a hierarchy must have a leader or [[root node|root]] that is common to all of the objects.
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| ==Mathematical representation==
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| {{Main|Hierarchy (mathematics)}}
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| Mathematically, in its most general form, a hierarchy is a [[partially ordered set]] or ''poset''.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|booktitle=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings
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| |isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The [[#Terminology|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 [[#Terminology|levels]] is referred to as a [[class (set theory)|class]].
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| "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a [[combinatorial]] [[object]].-->
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| 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 parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:
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| (2+5) x (7-4)=______
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| In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parenthesis is placed, one will know to do the operations within the parenthesis first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps in order to solve. The use of hierarchy in mathematics is beneficial in order 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.
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| ==Subtypes==
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| ===Nested hierarchy===<!--if you change this title, change the wiki links within the article that link to it!-->
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| [[File:Russian-Matroshka no bg.jpg|200px|right|thumb|[[Matryoshka doll]]s, also known as ''nesting dolls'' or ''Russian dolls''. Each doll is encompassed inside another until the smallest one is reached. This is the concept of ''nesting''. When the concept is applied to [[set (mathematics)|sets]], the resulting ordering is a ''nested hierarchy''.]]
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| A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of [[nested set]]s.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian [[matryoshka doll]]s. 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:
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| : <math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math>
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| 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.
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| Nested hierarchies are the organizational schemes behind [[Taxonomy (general)|taxonomies]] and systematic classifications. For example, using the original [[Linnaean taxonomy]] (the version he laid out in the 10th edition of ''[[Systema Naturae]]''), a human can be formulated as:<ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|authorlink=Carl Linnaeus|year=1959|edition=10th|language=[[Latin]]|url=http://www.biodiversitylibrary.org/bibliography/542#|location=[[Holmiae]]|publisher=Impensis Direct|isbn=0-665-53008-0|accessdate=2011-09-24}}</ref>
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| : <math>\text{H. sapiens} \subset \text{Homo} \subset \text{Primates} \subset \text{Mammalia} \subset \text{Animalia}</math>
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| Taxonomies may change frequently (as seen in [[biological classification|biological taxonomy]]), but the underlying concept of nested hierarchies is always the same.
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| 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.<ref name=Corballis>{{cite book |first=Michael |last=Corballis |title=The Recursive Mind |publisher=Princeton University Press |year=2011 |isbn=978-0691145471}}</ref>
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| ====Containment hierarchy====
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| A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this:
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| : <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math>
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| The notation <math> x \subsetneq y \, </math> means ''x'' is a subset of ''y'' but is not equal to ''y''.
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| A general example of a containment hierarchy is demonstrated in [[inheritance (computer science)|class inheritance]] in [[object-oriented programming]].
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| Two types of containment hierarchies are the ''subsumptive'' containment hierarchy and the ''compositional'' containment hierarchy. A subsumptive hierarchy "[[wikt:subsume|subsumes]]" its children, and a compositional hierarchy is "[[wikt:composed|composed]]" of its children. A hierarchy can also be both subsumptive ''and'' compositional.<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last=Kopisch|first=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>
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| =====Subsumptive containment hierarchy=====
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| A ''[[Category theory|subsumptive]]'' containment hierarchy is a classification of objects from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "[[is-a|IS-A]] hierarchy".<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|accessdate=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapterurl=http://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last=Funke|first=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref> 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, as are all [[systematic name|systematic naming]] schemes. Using again the example of Linnaean taxonomy, it can be seen that an object that is part 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 "[[concept]]s".<ref name="sys model"/> For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the [[wikt:conceptualization|conceptualization]] of an animal.
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| =====Compositional containment hierarchy=====
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| A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref> Most engineered structures, whether natural or artificial, can be broken down in this manner.
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| The compositional hierarchy that every person encounters at every moment is the [[hierarchy of life]]. Every person can be reduced to [[organ system]]s, which are composed of [[organ (anatomy)|organs]], which are composed of [[tissue (biology)|tissues]], which are composed of [[cells (biology)|cells]], which are composed of [[molecule]]s, which are composed of [[atom]]s. In fact, the last two levels apply to all [[matter]], at least at the [[macroscopic scale]]. Moreover, each of these levels inherit all the properties of their [[#Terminology|children]].
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| In this particular example, there are also ''[[emergent properties]]''—functions that are not seen at the lower level (e.g., [[cognition]] is not a property of [[neuron]]s but is of the [[Human brain|brain]])—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. These ''level hierarchies'' are characterized by bi-directional [[Causality|causation]].<ref name="natsocsci-ch4"/> ''Upward causation'' involves 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 causation]]'' refers to the effect that the incorporation of entity ''x'' into a higher-level entity can have on ''x'''s properties and interactions. Furthermore, the entities found at each level are ''[[autonomous]]''.
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| ==Contexts and applications==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
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| Almost every system within the world is arranged hierarchically.<ref name="electrodynamics">{{cite book|title=Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last=Kulish|first=V. V.|isbn=1-4020-0757-4|year=2002|volume=1|publisher=[[Springer Science+Business Media|Springer]]|pages=xvii-xx; 49–71}}</ref> By their common definitions, every [[nation]] has a government and every government is hierarchical.<ref>{{Cite book|contribution=government|title=Compact [[Oxford English Dictionary]]|url=http://www.askoxford.com/concise_oed/government?view=uk|isbn=978-0-19-861022-9|year=1991}}</ref><ref>{{Cite book|contribution=nation|title=Compact [[Oxford English Dictionary]]|url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991}}</ref> Socioeconomic systems are stratified into a social hierarchy (the [[social stratification]] of societies), and all [[systematic name|systematic classification schemes]] ([[Taxonomy (general)|taxonomies]]) are hierarchical. Most [[organized religion]]s, regardless of their internal governance structures, operate as a hierarchy under [[God]]. Many [[Christian denomination]]s have an [[autocephalous]] [[ecclesiastical hierarchy]] of leadership. Families are viewed as a hierarchical structure in terms of [[cousinship]] (e.g., first cousin once removed, second cousin, etc.), [[ancestry]] (as depicted in a [[family tree]]) and [[inheritance]] ([[order of succession|succession]] and [[heir]]ship). All the requisites of a well-rounded life and [[lifestyle (sociology)|lifestyle]] can be organized using [[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. [[Learning]] must often follow a hierarchical scheme—to learn [[differential equation]]s one must first learn [[calculus]]; to learn calculus one must first learn [[elementary algebra]]; and so on. Even [[nature]] itself has its own hierarchies, as demonstrated in numerous schemes such as [[Linnaean taxonomy]], the [[biological organisation|organization of life]], and [[biomass pyramid]]s. Hierarchies are so infused into daily life that they are viewed as trivial.<ref name="Dawkins"/><ref name="electrodynamics"/>
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| While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, all [[postal code]] systems are necessarily hierarchical. Using the [[Postal codes in Canada|Canadian postal code system]], the top level's binding concept is the "[[forward sortation area|postal district]]", and 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 an [[#Terminology|overlapping 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 format ''A0A 0A0''. Most [[library classification]] systems are also hierarchical. The [[Dewey Decimal System]] is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.<ref name="Dewey">{{cite journal|title=Tracking Nuclear Sources|date=May/June 2009|last=Walker|first=Randy|journal=[[Well Servicing]]|pages=28–30|url=http://wellservicingmagazine.com/sites/default/files/pdfmag/WSM_MAYJUN09.PDF|format=PDF}} See also [[Dewey Decimal System|Wikipedia article]].</ref>
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| [[File:Organizational chart.svg|thumb|200px|A simple [[hierarchical organization|organizational hierarchy]] depicted in the form of a [[tree structure|tree]]. Diagrams like this are called [[organizational chart]]s.]]
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| ===Organizations===
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| {{Main|Organizational structure|Hierarchical organization}}
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| [[Organization]]s can be structured using a hierarchy. In an organizational hierarchy, there is a single person or group with the most [[power (philosophy)|power]] and [[authority]], and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including [[government]]s, [[companies]], [[militia]] and [[organized religion]]s. The units or persons within an organization are depicted hierarchically in an [[organizational chart]].
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| In a [[reverse hierarchy]], the conceptual [[pyramid (geometry)|pyramid]] of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This model represents the idea that members of the higher rankings are responsible for the members of the lower rankings.
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| ===Computer graphic imaging===
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| Within most [[Computer-generated imagery|CGI]] and [[computer animation]] [[computer program|programs]] is the use of hierarchies. On a [[3D computer graphics|3D]] [[3d modeling|model]] of a [[human]], the [[chest]] is a [[parent]] of the upper left arm, which is a parent of the lower left arm, which is a parent of the [[hand]]. This is used in [[3D modeling|modeling]] and [[animation]] of almost everything built as a 3D [[Digital data|digital]] model.
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| ===Hierarchical verbal alignment===
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| {{Main|Direct–inverse language}}
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| Languages such as [[Cree language|Cree]] and [[Mapudungun language|Mapudungun]] distinguish subject and object on [[verb]]s not by different subject and object markers, but via a hierarchy of persons.
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| In this system, the three (or four with [[Algonquian languages]]) persons are placed in a hierarchy of [[salience (language)|salience]]. To distinguish which is subject and which object, ''inverse markers'' are used if the object outranks the subject.
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| In [[music]], the structure of a composition is often understood hierarchically (for example by [[Heinrich Schenker]] (1768–1835, see [[Schenkerian analysis]]), and in the (1985) [[Generative theory of tonal music|Generative Theory of Tonal Music]], by composer [[Fred Lerdahl]] and linguist Ray [[Jackendoff]]). 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 or [[Ursatz]], which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature.
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| The [[pitch (music)|pitches]] and [[Musical form|form]] of [[Tonality|tonal]] music are organized hierarchically, all pitches deriving their importance from their relationship to a [[Tonic (music)|tonic]] [[Key signature|key]], and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. [[Susan McClary]] connects this specifically in the [[sonata-allegro form]] to the feminist hierarchy of gender (see above) in her book ''Feminine Endings'', even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine."
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| ===Ethics, behavioral psychology, philosophies of identity===
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| [[File:Hierarchy Of Purposes.jpg|thumb|right|alt=|Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.]]
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| In [[ethics]], various [[virtues]] are enumerated and sometimes organized hierarchically according to certain brands of [[virtue theory]].
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| In all 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.
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| In the work of diverse theorists such as [[William James]] (1842–1910), [[Michel Foucault]] (1926–1984) and [[Hayden White]], important critiques of hierarchical [[epistemology]] are advanced. James famously asserts in his work "Radical Empiricism" that 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.
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| Hierarchy in ethics emerged in Western Europe, West Asia and North Africa around the 1600s. In this aspect, the term hierarchy refers to how distinguishable they are from real to unreal. [[Feminists]], [[Marxists]], [[anarchists]], [[communists]], [[critical theorists]] and 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. In some{{Which?|date=July 2012}} cultures, God can also be an addition to this hierarchy. However, feminists, Marxists, critical theorists and others analyze hierarchy in terms of the values and power that it arbitrarily assigns to one group over another. Hierarchical ethics offers a way of logical reasoning that is compatible with religious commitments. In some{{Which?|date=July 2012}} cultures, there is hierarchy within humanity. The dominant man in a family is above women, and children are after. In social classes, they are arranged as follows: king, civic officials, craftsmen, unskilled workers.
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| ===Further applications===
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| <!-- This section is for direct examples of a hierarchical system ONLY, and only ones that have not been summarized above. Methodologies belong in the appropriate section below. Related concepts are listed under the "See also" section. If you are uncertain where a link belongs, place it in the "See also" section. HINT: If you can't easily say what it's a hierarchy OF, it doesn't belong here (but that doesn't imply that if you can say what its a hierarchy of, it belongs here). -->
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| {{col-begin}}
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| {{col-3}}
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| ====Information-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "information-based hierarchies"-->
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| * [[Library classification]]
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| ** [[Dewey Decimal System]]
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| {{col-3}}
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| ====City planning-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "city planning-based hierarchies"-->
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| * [[Hierarchy of roads|Roads]]
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| ** [[Street hierarchy|Streets]]
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| * [[Settlement hierarchy]]
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| ** [[Settlement hierarchy#Example of a settlement hierarchy|As of 2010]]
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| ** [[Ekistic units|As of 2100 (estimate according to Doxiadis, 1968)]]
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| {{col-3}}
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| ====Linguistics-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "linguistics-based hierarchies"-->
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| * [[Tree model|Language family tree]]
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| * [[Levels of adequacy|Levels of adequacy for evaluating grammars]]
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| * [[Direct–inverse language]]s
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| * [[Structural linguistics]]
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| ** [[Parse tree]]
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| ** [[Formal grammar]]s
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| ** [[Abstract syntax tree]]
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| * [[Color terms#Basic color terms|Evolution of basic color terminology in languages]]
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| {{col-end}}
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| {{col-begin}}
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| {{col-3}}
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| ====Power- or authority-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "power- or authority-based hierarchies"-->
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| * [[Noble ranks|Aristocratic hierarchies]]
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| ** In [[Royal and noble ranks#General chart of "translations" between languages|Europe]]
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| ** In [[Chinese nobility#Princehood and peerage|China]]
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| * [[Ecclesiastical hierarchy|Ecclesiastical hierarchies]]
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| ** [[Catholic Church hierarchy]]
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| ** [[Priesthood (LDS Church)|LDS Church hierarchy]]
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| ** [[Kimbanguism#Hierarchy|Kimbanguist Church hierarchy]]
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| ** [[Raelism#Member hierarchy|Raelian Church hierarchy]]
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| ** see also [[autocephaly]]
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| * Administrative branch of government geographical hierarchies
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| ** [[Administrative divisions of China (disambiguation)|Administrative divisions of China]] <!--do NOT disambiguate-->
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| ** [[Administrative divisions of India]]
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| ** [[Administrative divisions of the United States]]
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| ** [[Administrative divisions of Russia]]
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| * Political party hierarchies
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| ** [[Ranks and insignia of the Nazi Party|Nazi Party]]
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| *** [[SS Ranks#Final SS ranks 1934–1945|SS]]
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| *** [[Glossary of Nazi Germany#G|Hierarchy of subdivisions within the Gau]]
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| ** [[Communist Party of the Soviet Union#Structure|Communist Party of the Soviet Union]]
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| ** [[Communist Party of China]]
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| * [[Command hierarchy|Chain of command]]
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| ** [[List of comparative military ranks|Military ranks]]
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| ** [[Military organization#Hierarchy of modern armies|Military units]]
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| ** [[Unified Combatant Command|U.S. Military Combatant Commands]]
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| * [[Dominance hierarchy|Intraspecial dominance]]
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| ** [[Pecking order]]
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| * [[Social stratification|Social classes]]
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| ** [[Caste system in India]]
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| ** [[Hierarchical structure of Feudal Japan]]
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| ** [[Master race#White racist hierarchy|White racist hierarchy]]
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| ** [[Hierarchy of Exclusion]] (Ender's Game)
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| {{col-3}}
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| ====Value-based====<!--value meaning both money and relative importance--><!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "value-based hierarchies"-->
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| * [[Hierarchy of genres|Art genres]]
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| * [[Hierarchy of evidence|Evidence]]
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| * [[Maslow's hierarchy of needs|Human needs]]
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| * [[Hierarchy of precious substances|Precious substances]]
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| * [[Hierarchy of values|Judicial hierarchy of social values]]
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| {{col-3}}
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| ====Perception-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "perception-based hierarchies"-->
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| * [[Color wheel]]
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| ** [[Primary colors]]
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| *** [[Secondary colors]]
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| **** [[Tertiary colors]]
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| {{col-end}}
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| {{col-begin}}
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| {{col-3}}
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| ====History-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "history-based hierarchies"-->
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| * [[Three-age system]]
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| * [[Comparative history|Cyclic theory of civilization]]
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| ** [[Spengler's civilization model|Oswald Spengler]]
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| ** [[A Study of History#List of civilizations|Arnold J. Toynbee]]
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| * [[Spiral dynamics]]
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| {{col-3}}
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| ====Science-based====
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| <!--[[WP:HYPHEN]]—this category's logical title is "science-based hierarchies"-->
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| * [[Earth's location in the universe#Earth in the universe|Hierarchy of organization within the Universe]]
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| * [[Orders of magnitude]]
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| * [[Energy quality]]
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| * [[Hierarchy of knowledge|Scientific knowledge]]
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| * [[Hierarchical ternary star system|Star systems]]
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| * [[Biological classification]]
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| * [[Biological organization]]
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| * [[Phylogenetic tree]]
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| * [[Timeline of evolution|Evolutionary development]]
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| * [[Ecological land classification#Hierarchy of classification levels in ecology compared to other fields|Hierarchy of ecological georegions]]
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| {{col-3}}
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| ====Technology-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "technology-based hierarchies"-->
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| * [[Hierarchical clustering|Clusters]]
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| * [[Hierarchy (object-oriented programming)|Class constructs]]
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| * [[Hierarchical database model|Data organization]]
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| ** [[Hierarchical query]]
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| * [[Hierarchical Data Format|Data storage]]
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| ** [[Hierarchical File System|Computer files (Macintosh)]]
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| * [[Hierarchical control system|Devices]]
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| * [[Classless inter-domain routing|IP addresses]]
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| * [[Memory hierarchy|Memory]]
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| ** [[Hierarchical page tables|Virtual memory allocation]]
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| * [[Hierarchical internetworking model|Networks]]
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| * [[Hierarchical cell structure|Radio cells]]
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| * [[Hierarchical state machine|States (configurations)]]
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| * [[Hierarchical name space|Web addresses]]
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| * [[Structure]]
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| ** [[Data Structure]]
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| {{col-end}}
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| ====Religion- and mythology-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "religion- and mythology-based hierarchies"-->
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| * Levels of consciousness
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| ** [[Chakra#The seven major chakras|Chakras]]
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| ** [[Great chain of being]]
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| ** [[Ray of Creation|G.I. Gurdjieff]]
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| ** [[Eight Circuit Model of Consciousness#The eight circuits|Timothy Leary]]
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| * Levels of spiritual development
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| ** In [[Four stages of enlightenment|Theravada Buddhism]]
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| ** In [[Bhumi (Buddhism)|Mahayana Buddhism]]
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| ** In [[Initiation (Theosophy)|Theosophy]]
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| * Ages in the evolution of society
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| ** In [[Astrological age#Past ages|Astrology]]
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| ** In [[Ages of Man|Hellenism (the Ancient Greek Religion)]]
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| ** [[Dispensation (period)#Protestant dispensations|Dispensations in Protestantism]]
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| ** [[Dispensation (period)#Latter Day Saint dispensations|Dispensations in Mormonism]]
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| * [[Hierarchical communion|Degrees of communion between various Christian churches]]
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| * [[UFO religion]]s
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| ** [[Master Jesus#Airborne Division of the Brotherhood of Light|Command hierarchy of the ''Ashtar Galactic Command'' flying saucer fleet]]
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| * Deities
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| ** In [[Japanese Buddhist pantheon#Hierarchical structure of the Buddhist pantheon|Japanese Buddhism]]
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| ** In [[Spiritual Hierarchy#Levels of the spiritual hierarchy|Theosophy]]
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| * Angels
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| ** In [[Christian angelic hierarchy|Christianity]]
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| ** In [[Islamic view of angels#Angel hierarchy|Islam]]
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| ** In [[Jewish angelic hierarchy|Judaism]]
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| *** [[Kabbalistic angelic hierarchy|Kabbalistic]]
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| ** In [[Yazata|Zoroastrianism]]
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| * Devils and Demons
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| ** [[Hierarchy of devils|Devils]]
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| ** [[Hierarchy of demons|Demons]]
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| * [[Hell]]s
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| ** In [[Inferno (Dante)|Catholicism (Nine Levels of Hell)]]
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| ** In [[Naraka (Buddhism)|Buddhism (Sixteen Levels of Hell)]]
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| * [[Religious stratification|Religions in society]]
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| * (organizational hierarchies are listed under {{nowrap|"[[#Power- or authority-based|Power- or authority-based]]"}})<!--non-breaking spaces used for neatness at all resolutions-->
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| ===Methods using the hierarchical model===<!-- See note at "Further applications"-->
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| {{columns-list|3|
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| * [[Analytic Hierarchy Process]]
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| ** [[Hierarchical Decision Process]]
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| * [[HOOD method|Hierarchic Object-Oriented Design]]
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| * [[Hierarchical Bayes model]]
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| * [[Hierarchical clustering]]
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| ** [[Hierarchical clustering of networks]]
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| * [[Hierarchical constraint satisfaction]]
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| * [[Hierarchical linear modeling]]
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| * [[Hierarchical modulation]]
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| * [[Hierarchical proportion]]
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| * [[Hierarchical RBF|Hierarchical radial basis function]]
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| * [[Hierarchical storage management]]
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| * [[Hierarchical task network]]
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| * [[Hierarchical temporal memory]]
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| * [[Hierarchical Token Bucket|Hierarchical token bucket]]
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| * [[Hierarchical visitor pattern]]
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| * [[Presentation-abstraction-control]]
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| ** [[Hierarchical-Model-View-Controller]]
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| }}
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| ==See also==<!-- See note at "Further applications"-->
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| {{columns-list|3|
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| * [[Form of government]]
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| * [[Anarchy]]
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| * [[Graph theory]]
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| * [[Heterarchy]]
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| * [[Hierarch]]
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| ** [[Hierarch of all Hierarchs]]
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| ** [[Hierarchs (Halo)|Hierarchs]]
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| * [[Hierarchical classifier]]
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| * [[Hierarchical epistemology]]
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| * [[Hierarchical hidden Markov model]]
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| * [[Hierarchical incompetence]]
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| * [[Hierarchical INTegration]]
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| * [[Hierarchical Music Specification Language]]
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| * [[Hierarchical protection domains]]
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| * [[Hierarchy Open Service Interface Definition]]
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| * [[Hierarchy problem]]
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| * [[HierarchyBrowser]]
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| * [[Multilevel model]]
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| * [[Peter Principle]]
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| * [[Social Dominance Theory]]
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| }}
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| ==Footnotes==
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| {{reflist|2}}
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| ==Further reading==
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| * {{cite book|first=Valerie|last=Ahl|first2=Timothy F. H.|last2=Allen|authorlink2=Timothy F. H. Allen|year=1996|title=Hierarchy Theory|location=New York|publisher=Columbia University Press|isbn=0-231-08481-1}}
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| * {{cite conference|last=Akl|first=Selim G.|authorlink=Selim Akl|last2=Taylor|first2=Peter D.|title=Cryptographic solution to a multilevel security problem|booktitle=Advances in Cryptology: Proceedings of [[CRYPTO]] '82|pages=237–249|publisher=[[Plenum Publishing Corporation]]|year=1983|location=New York|url=http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C82/237.PDF|format=PDF|isbn=0-306-41366-3}}{{dead link|date=September 2011}}
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| * {{cite journal|title=Regulatory hierarchies in auxin signal transduction and vascular tissue development|last=Ckurshumova|first=Wenzislava|isbn=978-0-494-27682-2|year=2007|journal=Dissertation Abstracts International|volume=68|issue=5|page=section B|place=University of Toronto|publication-place=|format=Ph.D. dissertation}}
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| * {{Cite book|last1=Galindo|first1=Cipriano|last2=Fernández-Madrigal|first2=Juan-Antonio|title=Multiple Abstraction Hierarchies for Mobile Robot Operation in Large Environments|series=Studies in Computational Intelligence|editor-last=Kacprzyk|editor-first=Janusz|year=2007|publisher=Springer Berlin Heidelberg|location=Berlin|isbn=978-3-540-72688-3}}
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| * {{cite journal|first=Julie|last=Nelson|authorlink=Julie Nelson (economist)|year=1992|title=Gender, Metaphor and the Definition of Economics|journal=Economics and Philosophy|volume=8|issue=1|pages=103–25|doi=10.1017/S026626710000050X}}
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| * {{cite book|last=Pumain|first=Diane|title=Hierarchy in Natural and Social Sciences|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}
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| * {{cite book|first=A.|last=Rosenbaum|authorlink=Alexis Rosenbaum|year=2000|title=Les représentations hiérarchiques en philosophie|language=French|location=Paris|publisher=Desclee de Brouwer}}
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| * {{cite journal|title=Improving classification models when a class hierarchy is available|last=Shahbaba|first=Babak|isbn=978-0-494-28076-8|journal=Dissertation Abstracts International|volume=68|issue=6|page=section B|place=University of Toronto|publication-place=|format=Ph.D. dissertation|year=2007}}
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| ** Also includes full copies of:
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| ** {{cite journal|title=Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior|last=Shahbaba|first=Babak|last2=Neal|first2=Radford M.|journal=Bayesian Analysis|volume=2|issue=1|pages=221–228|year=2007|issn=1936-0975|publisher=[[International Society for Bayesian Analysis]]|location=[[Carnegie Mellon University]], Pittsburgh, Pennsylvania|url=http://ba.stat.cmu.edu/journal/2007/vol02/issue01/shahbaba.pdf|format=PDF}}
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| ** {{cite journal|last=Shahbaba|first=Babak|last2=Neal|first2=Radford M.|title=Gene function classification using Bayesian models with hierarchy-based priors|journal=[[BMC Bioinformatics]]|publisher=[[BioMed Central]]|location=London, England|year=2006|volume=7|page=448|doi=10.1186/1471-2105-7-448|pmc=1618412|pmid=17038174|issn=1471-2105}}
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| ==External links==
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| * [http://www.isss.org/hierarchy.htm Principles and annotated bibliography of hierarchy theory]
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| * [http://www.nbi.dk/~natphil/salthe/Summary_of_the_Principles_o.pdf Summary of the Principles of Hierarchy Theory] — S.N. Salthe
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| * [http://hierarchy-chart.com/ Everything is Hierarchical] - Think in a different way.
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| [[Category:Hierarchy|*]]
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| [[Category:Patterns]]
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| [[Category:Structure]]
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| [[Category:Political culture]]
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