http://www.learnthat.com/define/view.asp?id=2772
"A classification of relationships in which each item except the top one (known as the root) is a specialized form of the item above it. Each item can have one or more items below it in the hierarchy. In the Java class hierarchy, the root is the Object class." - Hierarchy as specialisation.
http://dev.fyicenter.com/Interview-Questions/J2SE/What_is_hierarchy.html
"A is system of ranking and organizing things. Different fields use the word in slightly different ways, but a particular definition, which the article will attempt first, captures the core of almost all uses. Originally, "hierarchy" was a word meaning "rule by priests". Since hierarchical churches such as the Roman Catholic and Eastern Orthodox churches had tables of organization that were "hierarchical" in the modern sense of the word, the term came to refer to more general organizational methods.
Illustration: A hypothetical hierarchical organization for an encyclopedia. Each node "contains" all the sections below it, e.g. the culture section contains the art section and the craft section.
General considerations (informal)
A precise, mathematical definition of hierarchy will be given in the next section. This section will try to explore the ideas behind that more compact definition.
A hierarchy is based on an asymmetrical relationship, such as "is the boss of", "is part of", or "is better than". Such relationships are "asymmetrical" in the sense that if they "work one way", they don't "work the other". For example, if Sally is the boss of Jim, then Jim is not the boss of Sally. When two nodes are related, one is designated the "superior" (or sometimes the "parent") and the other the "subordinate" (or sometimes the "child"). In the intuitive case of the "is the boss of" relation, the boss is the superior and the employee is the subordinate.
A hierarchy's asymmetrical relationship can link entities in one of three ways: directly, indirectly, or not at all. The illustration shows a direct link between the craft and culture sections; the craft section is directly linked to the culture section by the "contains" relationship. This is akin to how your boss in directly in charge of you. In contrast, the illustration shows an indirect link between craft and encyclopedia; the craft section is only "contained" by the encyclopedia as a whole by virtue of being "contained" by the culture section. This is akin to how the CEO of a company is in charge of a factory worker only via middle management. Finally, there is effectively no link between the art and the craft sections; neither section contains the other. This is akin to two co-workers, neither of whom is the other's boss.
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Every member is reachable from any other by following the relationship in either direction, but there is no way of coming back to a particular member by always following the relationship in the same direction.
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General considerations (formal)
A hierarchy can thus be represented as a connected directed acyclic graph.
Examples of reasoning with hierarchies
Many aspects of the world are analyzed, arguably fruitfully, from a hierarchical perspective. Science provides the following examples:
- In biology, organisms are commonly described as an assembly of parts (organs) which are themselves assemblies of yet smaller parts, and so on.
- In physics, the standard model decomposes bodies down to their smallest particle components.
- In linguistics, words or sentences are often broken down into hierarchies of parts and wholes.
In all of these examples, the asymmetric relationship is "is composed of".
Social hierarchies
Many human organizations, such as businesses, churches, armies and political movements are structured hierarchically, at least officially; commonly superiors, called bosses, have more power than their subordinates. Thus the asymmetrical relationship might be "has power over". (Some analysists question whether power "really" works as the traditional organizational chart indicates, however.)
Feminists talk about a hierarchy of gender, in which a culture sees males or masculine traits as superior to females or feminine traits. In the terms above, these feminists present us a hierarchy of only two nodes, "masculine" and "feminine", connected by the asymmetrical relationship "is valued more highly by society". An example of this usage:
- The hierarchical nature of the dualism - the systematic devaluation of females and whatever is metaphorically understood as "feminine" - is what I identify as sexism. (Nelson 1992, p. 106)
Note that when feminists and other social critics use the word hierarchy, they usually hope to evoke negative connotations; hierarchy, for them, is a bad thing. In these contexts, hierarchy and power structure are basically synonyms.
Hierarchical nomenclatures in the arts and sciences
Hierarchy is often used to control complexity in engineering endeavors. In object-oriented programming, for example, classes are organized hierarchically; the relationship between two related classes is called inheritance.
The pitches and form of Tonal music are organized hierarchically, all pitches deriving their importance from their relationship to a tonic key, and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. 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."
Wikis
The Wikipedia community is noteworthy for being not overtly hierarchically structured, as no contributor possesses inherently higher standing than another, excepting certain limited "admin" and "developer" powers restricted to a few. However, some would counter that although there is no explicit hierarchy there are social norms which make contributions unequal, as some contributors have more influence because their edits command higher respect.
Those who frequent Wikis might label Wikipedia's organization "wikiarchical".
The concept of hierarchy qualifies as interdisciplinary.
History of the word
From the greek hieros, sacred + archos, ruler.
External link
Principles and annotated bibliography of hierarchy theory
Generalizations: Structure
Specializations:
- purpose: hierarchical organization
- structural properties: hierarchical tree structure, rooted hierarchy
- nature of the hierarchical relationship: part-whole hierarchy, containment hierarchy, inheritance hierarchy, responsibility hierarchy, control hierarchy
Relevant examples:
- Biology: Linnaean taxonomy
- Genealogy: genealogy tree
- Linguistics: Chomsky hierarchy
- Psychology: Maslow hierarchy of needs" - Hierarchy explained in-depth.
http://knowledgerush.com/kr/encyclopedia/Hierarchy/"A SUMMARY OF THE PRINCIPLES OF HIERARCHY THEORY
The Hierarchy theory is a dialect of general systems theory. It has emerged as part of a movement toward a general science of complexity. Rooted in the work of economist, Herbert Simon, chemist, Ilya Prigogine, and psychologist, Jean Piaget, hierarchy theory focuses upon levels of organization and issues of scale. There is significant emphasis upon the observer in the system.
Hierarchies occur in social systems, biological structures, and in the biological taxonomies. Since scholars and laypersons use hierarchy and hierarchical concepts commonly, it would seem reasonable to have a theory of hierarchies. Hierarchy theory uses a relatively small set of principles to keep track of the complex structure and a behavior of systems with multiple levels. A set of definitions and principles follows immediately:
Hierarchy: in mathematical terms, it is a partially ordered set. In less austere terms, a hierarchy is a collection of parts with ordered asymmetric relationships inside a whole. That is to say, upper levels are above lower levels, and the relationship upwards is asymmetric with the relationships downwards.
Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.
Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.
Level of observation: this type of level fits into its hierarchy by virtue of relative scaling considerations. For example, the host of a skin parasite represents the context for the population of parasites; it is a landscape, even though the host may be seen as belonging to a level of organization, organism, that is lower than the collection of parasites, a population.
The criterion for observation: when a system is observed, there are two separate considerations. One is the spatiotemporal scale at which the observations are made. The other is the criterion for observation, which defines the system in the foreground away from all the rest in the background. The criterion for observation uses the types of parts and their relationships to each other to characterize the system in the foreground. If criteria for observation are linked together in an asymmetric fashion, then the criteria lead to levels of organization. Otherwise, criteria for observation merely generate isolated classes.
The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply. Upper levels are above lower levels by virtue of: 1) being the context of, 2) offering constraint to, 3) behaving more slowly at a lower frequency than, 4) being populated by entities with greater integrity and higher bond strength than, and 5), containing and being made of - lower levels.
Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.
Duality in hierarchies: the dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole. Arthur Koestler in his "Ghost in The Machine" referred to the notion of holon, which means an entity in a hierarchy that is at once a whole and at the same time a part. Thus a holon at once operates as a quasi-autonomous whole that integrates its parts, while working to integrate itself into an upper level purpose or role. The lower level answers the question "How?" and the upper level answers the question, "So what?"
Constraint versus possibilities: when one looks at a system there are two separate reasons behind what one sees. First, it is not possible to see something if the parts of the system cannot do what is required of them to achieve the arrangement in the whole. These are the limits of physical possibility. The limits of possibility come from lower levels in the hierarchy. The second entirely separate reason for what one sees is to do with what is allowed by the upper level constraints. An example here would be that mammals have five digits. There is no physical reason for mammals having five digits on their hands and feet, because it comes not from physical limits, but from the constraints of having a mammal heritage. Any number of the digits is possible within the physical limits, but in mammals only five digits are allowed by the biological constraints. Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility. Forget the distinction, and biology becomes pointlessly confused, impossibly complicated chemistry, while chemistry becomes unwieldy physics.
Complexity and self-simplification: Howard Pattee has identified that as a system becomes more elaborately hierarchical its behavior becomes simple. The reason is that, with the emergence of intermediate levels, the lowest level entities become constrained to be far from equilibrium. As a result, the lowest level entities lose degrees of freedom and are held against the upper level constraint to give constant behavior. Deep hierarchical structure indicates elaborate organization, and deep hierarchies are often considered as complex systems by virtue of hierarchical depth.
Complexity versus complicatedness: a hierarchical structure with a large number of lowest level entities, but with simple organization, offers a low flat hierarchy that is complicated rather than complex. The behavior of structurally complicated systems is behaviorally elaborate and so complicated, whereas the behavior of deep hierarchically complex systems is simple.
Hierarchy theory is as much as anything a theory of observation. It has been significantly operationalized in ecology, but has been applied relatively infrequently outside that science. There is a negative reaction to hierarchy theory in the social sciences, by virtue of implications of rigid autocratic systems or authority. When applied in a more general fashion, even liberal and non-authoritarian systems can be described effectively in hierarchical terms. There is a politically correct set of labels that avoid the word hierarchy, but they unnecessarily introduce jargon into a field that has enough special vocabulary as it is." - Hierarchy as theory.
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