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Analytical hierarchy information


In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of second-order arithmetic, which can have quantifiers over both the set of natural numbers, , and over functions from to . The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projective hierarchy.

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Analytical hierarchy

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descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas...

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Analytic hierarchy process

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In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and...

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Arithmetical hierarchy

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hyperarithmetical hierarchy and the analytical hierarchy extend the arithmetical hierarchy to classify additional formulas and sets. The arithmetical hierarchy assigns...

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Hierarchy

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that are being arranged hierarchically (e.g., an administration) Dimension: another word for "system" from on-line analytical processing (e.g. cubes)...

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Phonological hierarchy

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slightly different hierarchies. For instance, there is one hierarchy which is primarily used in theoretical phonology, while a similar hierarchy is used in discourse...

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Projective hierarchy

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classified by the projective hierarchy are exactly the sets classified by the relativized version of the analytical hierarchy. This relationship is important...

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Polynomial hierarchy

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arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH. Classes within the hierarchy have...

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Analytic

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Look up analytic, analytical, or analyticity in Wiktionary, the free dictionary. Analytic or analytical may refer to: Analytical chemistry, the analysis...

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Delta

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classification in the arithmetical hierarchy Δ n 1 {\displaystyle \Delta _{n}^{1}} , a classification in the analytical hierarchy Δ i P {\displaystyle \Delta...

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SMART criteria

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"Prioritization of key performance indicators: An integration of analytical hierarchy process and goal setting". International Journal of Productivity...

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Analytic set

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counterpart Σ 1 1 {\displaystyle \Sigma _{1}^{1}} (see analytical hierarchy). The complements of analytic sets are called coanalytic sets, and the set of coanalytic...

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Descriptive set theory

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of hierarchies of classical descriptive set theory. Thus the hyperarithmetic hierarchy is studied instead of the Borel hierarchy, and the analytical hierarchy...

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The Analytical Language of John Wilkins

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Borges's "The analytical language of John Wilkins"". Orbis Litterarum. 67 (3): 193–218. doi:10.1111/j.1600-0730.2011.01049.x. The Analytical Language of...

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Analytic network process

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The analytic network process (ANP) is a more general form of the analytic hierarchy process (AHP) used in multi-criteria decision analysis. AHP structures...

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Super Decisions

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decision making methods. Super Decisions implements the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP). It has been used in many research...

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Borel hierarchy

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in the lightface Borel hierarchy if and only if it is at level Δ11{\displaystyle \Delta _{1}^{1}} of the analytical hierarchy. These sets are also called...

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Definable real number

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definitions of arithmetical and analytical reals can be stratified into the arithmetical hierarchy and analytical hierarchy. In general, a real is computable...

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Hierarchy theory

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the pre-analytical choices of the observer. Instead of analyzing the whole structure, hierarchy theory refers to the analysis of hierarchical levels,...

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International Symposium on the Analytic Hierarchy Process

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Symposium on the Analytic Hierarchy Process (ISAHP) is a biennial conference on multi-criteria decision analysis, particularly the analytic hierarchy process (AHP)...

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List of mathematical logic topics

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set Descriptive set theory Analytic set Analytical hierarchy Borel equivalence relation Infinity-Borel set Lightface analytic game Perfect set property...

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Ernest Forman

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Expert Choice and developed the first commercial implementation of the Analytic Hierarchy Process. Forman's work has been focused on executive decision-making...

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Ecological footprint

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(ed.). "An integrated approach of Ecological Footprint (EF) and Analytical Hierarchy Process (AHP) in human ecology: A base for planning toward sustainability"...

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