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# Topic: Analytical hierarchy

###### In the News (Thu 20 Jun 13)

 Arithmetical hierarchy - Wikipedia, the free encyclopedia In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies the set of arithmetic formulas (or arithmetic sets) according to their degree of solvability. Layers in the hierarchy are defined as those formulas which satisfy a proposition (description) of a certain complexity. The polynomial hierarchy is a "feasible resource-bounded" version of the arithmetical hierarchy, in which polynomial length bounds are placed on the strings involved, or equivalently, polynomial time bounds are placed on the Turing machines involved. en.wikipedia.org /wiki/Arithmetical_hierarchy   (325 words)

 PlanetMath: analytic hierarchy   (Site not responding. Last check: 2007-10-20) The analytic hierarchy is a hierarchy of either (depending on context) formulas or relations similar to the arithmetical hierarchy. Like the arithmetical hierarchy, the relations in each level are exactly the relations defined by the formulas of that level. This is version 1 of analytic hierarchy, born on 2002-08-17. planetmath.org /encyclopedia/AnalyticHierarchy.html   (124 words)

 Analytical hierarchy - Encyclopedia, History, Geography and Biography In mathematical logic and descriptive set theory, the analytical hierarchy is a second-order analogue of the arithmetical hierarchy. The standard notation $\Sigma^1_0 = \Pi^1_0 = \Delta^1_0$ indicates on the one hand the class of formulas that can be expressed as formulas of arbitrary finite length of alternating universal and existential quantifiers for individuals over predicates linked by sentential connectives; and on the other the class of Borel sets. A $\Sigma^1_1$ set is said to be analytic, and can thus be seen as a projection of a Borel set. www.arikah.net /encyclopedia/Analytic_set   (378 words)

 COMM80 - Risk Assessment and Management of Change - Analytic Hierarchy Process   (Site not responding. Last check: 2007-10-20) The concept behind the hierarchy is that it is possible to judge the relative importance of the elements in a given level with respect to some or all of the elements in the level above. The hierarchy can be used either bottom up at making judgements to learn from the activities the importance of the objectives, or from the top down when the priorities of the objectives are set in advance, for example by previous experience. The Analytic Hierarchy Process does not require a unified scale since it derives scales for each factor that are ratio scales, these are then made commensurate through the hierarchical weighting process. osiris.sunderland.ac.uk /risk/content/pass/material/ahp.html   (1287 words)

 Analytical hierarchy - Wikipedia, the free encyclopedia In mathematical logic and descriptive set theory, the analytical hierarchy is a second-order analogue of the arithmetical hierarchy; it thus continues the classification of sets and properties by their complexity to levels higher than can be defined using first-order logic. Note that the Greek letters here should be read as lightface symbols; the corresponding boldface symbols indicate the class of first-order formulas which can be written with real parameters; see projective hierarchy for more details. set can be seen as a lightface or recursive analog of an analytic set, since it is an arithmetic projection of an arithmetic relation, just as an analytic set is an arbitrary projection of a Borel relation. en.wikipedia.org /wiki/Analytical_hierarchy   (235 words)

 GIS/EM4 - Integrating the Analytical Hierarchy Process with GIS to capture expert knowledge for Land Capability ... This paper examines the nature of this complexity and focuses on the utility of the Analytical Hierarchy Process (AHP) as a tool for capturing expert knowledge on environmental systems where data may be lacking. An example of the hierarchy for biophysical capability for carrots in West Gippsland is shown in figure 1. The process of building a decision hierarchy using the AHP method is effective and captures expert knowledge in form that is transparent, of value to the experts building the decision hierarchy and promotes focussed and detailed discussion on each criterion. www.colorado.edu /research/cires/banff/pubpapers/133   (3372 words)

 [No title]   (Site not responding. Last check: 2007-10-20) Moreover, such analytical quality specifications should be firmly based upon medical requirements, useable in all laboratories irrespective of size, type or location, generated using simple to understand models, and widely accepted as cogent by professionals in the field. In contrast, if the analytical method had positive bias, the glycated haemoglobin would appear lower: the clinician might congratulate the patient on maintaining good control but, while the risk of microalbuminuria might be lower, the risk of hypoglycaemic episodes might be increased. Measures of the quality of analytical performance could be obtained be comparison with attainment documented in published works on similar or other assay methods for the quantity for which quality specifications were required. www.ifcc.org /eJIFCC/vol13no1/1301200106n.htm   (2990 words)

 SAE Technical Paper Template Relative risk is calculated as follows: For each branch of the hierarchy, the risk factor weights along the branch are multiplied times the input value at the lowest level to compute the contribution of this input to the overall risk assessment for the flight under consideration. The Analytic Hierarchy Process was identified as a methodology for the elicitation and representation of expert knowledge in the two categories. As the hierarchy was developed, it became clear that extensive datasets will be required to develop systemic values, i.e., average values of many risk factors derived from the entire operation, as well as real-time connections to various flight operations databases. www.nrlmry.navy.mil /foras/publications/ASC99-paper.html   (3826 words)

 Analytical hierarchy -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-20) Analytical hierarchy -- Facts, Info, and Encyclopedia article A set is said to be analytic, and can thus be seen as a (Any structure that branches out from a central support) projection of a Borel set. Then we may define "second projective" sets as projections of first projective sets or complements thereof, producing the set of asets, and so on. www.absoluteastronomy.com /encyclopedia/a/an/analytical_hierarchy.htm   (239 words)

 DSS News: Vol. 4, No. 13 At the top of the hierarchy is the overall objective and the decision alternatives are at the bottom. The number of levels in the hierarchy depends on the complexity of the problem and the decision maker's model of the problem hierarchy. The analytical hierarchy created in Expert Choice can be used to support ranking tasks like rank ordering the importance of military targets, the quality of research proposals or the quality of investment proposals. dssresources.com /newsletters/82.php   (1644 words)

 ipedia.com: Arithmetical hierarchy Article   (Site not responding. Last check: 2007-10-20) In mathematical logic, the arithmetical hierarchy classifies the set of all formulas according to their degree of solvability. In mathematical logic, the arithmetical hierarchy (also known as the arithmetic hierarchy) classifies the set of all formulas (or functions) according to their degree of solvability. See also: recursion theory, analytical hierarchy, interpretability logic. www.ipedia.com /arithmetical_hierarchy.html   (271 words)

 Using analytical hierarchy process and fuzzy set theory to rate and rank the disability   (Site not responding. Last check: 2007-10-20) Therefore, in order to place qualified disabled people in appropriate job positions, a multidimensional assessment method should be developed for measuring and interpreting the disabled people's residual capabilities with respect to their strengths, weaknesses, and their compatibility to job requirements and work environments. Thus, the primary purpose of this study is to discuss how to structure a hierarchy related to the problem of deriving an Overall Disability Index (ODI) for measuring the individual's disability. The analytical hierarchy process, along with the entropy theory and fuzzy set theory, is applied for eliciting the weights among the attributes and aggregating the multiple attributes into a single measurement. www.uwv.nl /cba/module8/meta24176.htm   (213 words)

 Incorporating Community Preferences in Local Development Strategies The Analytical Hierarchy Process (AHP) was used to elicit community leaders’ preferences for seven economic and non-economic industry impacts: number of jobs, average wage or salary, level of capital investment, level of utility requirements, impacts of population growth, impacts on property values, and cleanliness of industry. Contrary to what is often reported in the media, the results indicate that the number of jobs created by the establishment of new industry may not be the most important goal of a community. Beyond the industrial recruitment model, the Analytical Hierarchy Process offers a valuable tool to communities that are faced with making decisions involving complex or multiple objectives. www.cpac.missouri.edu /newsuse/archive/980518.html   (730 words)

 ISNAR - Discussion Forum on Priority Setting in Agricultural Research   (Site not responding. Last check: 2007-10-20) The analytic hierarchy process (AHP) is a comprehensive, logical and structural framework, which allows to improve the understanding of complex decisions by decomposing the problem in a hierarchical structure. The first step is to structure the decision problem in a hierarchy as depicted in Figure 1. The next level consists of the criteria relevant for this goal and at the bottom level are the alternatives (for example research projects) to be evaluated. www.cgiar.org /ISNAR/Fora/Priority/MeAnalit.htm   (756 words)

 bp_render_qam_8|Module 1: Analytical Hierarchy Process|True or False The Analytic Hierarchy Process would probably be preferable to the Multifactor Evaluation Process when trying to determine which R&D projects should be funded. Decision situations where we easily and accurately determine various weighting factors are excellent candidates for the Analytic Hierarchy Process analysis. In the analytic hierarchy process we rate each pair of alternatives using a 13-point scale. wps.prenhall.com /bp_render_qam_8/0,,400262-,00.utf8.html   (141 words)

 Analytical Hierarchy Process It is based on the assumption that when faced with a complex decision the natural human reaction is to cluster the decision elements according to their common characteristics. This gives a weighting for each element within a cluster (or level of the hierarchy) and also a consistency ratio (useful for checking the consistency of the data). The Analytical Hierarchy Process Model was designed by TL Saaty as a decision making aid. www.ifm.eng.cam.ac.uk /dstools/choosing/ahp.html   (160 words)

 Information Bridge: DOE Scientific and Technical Information   (Site not responding. Last check: 2007-10-20) WSRC was requested to evaluate whether nuclear materials other than aluminum-clad spent nuclear fuel should be considered for treatment to prepare them for disposal in the melt and dilute facility as part of the Treatment and Storage Facility (TSF) currently projected for construction in the L-Reactor process area. The Analytical Hierarchy Process using a ratings methodology was used to rank potential feed candidates for disposition through the Melt and Dilute facility proposed for disposition of Savannah River Site aluminum-clad spent nuclear fuel. Because of the scoping nature of this analysis, the expert team convened for this purpose concentrated on technical feasibility and potential cost impacts associated with using melt and dilute versus the current disposition option. www.osti.gov /bridge/product.biblio.jsp?osti_id=752142   (214 words)

 Ducks In Order™ Blog: Background: Analytical Hierarchy Process The Analytical Hierarchy Process is a technique for evaluating the factors that make up a decision. If you are going to use some sort of tool to rank your options, you need to tell that tool how much weight to give to each of the factors. The Analytical Hierarchy Process is a way to determine those weights. ducksinorder.blogspot.com /2004/10/background-analytical-hierarchy.html   (644 words)

 IngentaConnect An analytical hierarchy process framework for comparing the overa...   (Site not responding. Last check: 2007-10-20) But the use of non-financial performance measures makes it difficult to assess and compare the overall effectiveness of each manufacturing department, in terms of support provided to the achievement of the manufacturing strategy, since to this aim it is necessary to integrate performance measures expressed in heterogeneous measurement units. Aims to show the potential of the analytical hierarchy process (AHP) for assessing and comparing the overall manufacturing performance of different departments. Does not report the detailed analytical description of the AHP but focuses on the practical problems and managerial implications related to its application to performance measurement, pointing out also its assumptions and limitations. www.ingentaconnect.com /content/mcb/024/1996/00000016/00000008/art00006   (227 words)

 MNL29 - Analytical Hierarchy Process to Multiattribute Analysis (ASTM) This software product supports the application of ASTM's AHP (Analytical Hierarchy Process) standard practice (E 1765) for performing multiattribute decision analysis to evaluate buildings and building systems. It includes a comprehensive list of building-related attributes (developed by ASTM Subcommittee E06.25 and E06.81) in a glossary from which users can select attributes of interest when evaluating their building decision. The Analytical Hierachy Process is the source of the underlying mathematical theory for the Program; such technology is included in the Program under license from Expert Choice, Inc. The program is protected by U.S. Patent No. 4613946. www.normas.com /ASTM/BOOKS/MNL29.html   (267 words)

 [No title]   (Site not responding. Last check: 2007-10-20) I will demonstrate that embedding the MRCM within an Analytical Hierarchy Process (AHP) model eliminates arbitrary scaling problems and allows for the refinment of the MRCM by making it easy to weight not only all the Maxwell Criteria but also easy to scale each of the individual criterion's location continua. THE ANALYTICAL HIERARCHY PROCESS (AHP) The Analytical Hierarchy Process (AHP) allows for the modeling of criteria involved in influencing the outcome of any decision. Once the hierarchy is developed all that remains is the ratings of the selections. www.losangeles.af.mil /Tenants/SCEA/CRIMS/crimgde7.doc   (1787 words)

 Analytical Hierarchy Process :: Overview from The Quality Portal Developed by Thomas Saaty, AHP provides a proven, effective means to deal with complex decision making and can assist with identifying and weighting selection criteria, analyzing the data collected for the criteria and expediting the decision-making process. Relative scores for each choice are computed within each leaf of the hierarchy. Scores are then synthesized through the model, yielding a composite score for each choice at every tier, as well as an overall score. thequalityportal.com /q_ahp.htm   (347 words)

 [No title]   (Site not responding. Last check: 2007-10-20) Broad technical and analytical proficiency is required across all program areas such as munitions cost analysis, operational flight test currency resource reporting and control, aircraft modification schedule/cost reviews, and mission area plan analyses. The contractor may from time-to-time be required to react on short notice to critical time sensitive issues that are within the scope of this task order. The contractor shall provide technical and analytical assistance to assess weapon system capabilities using strategy-to-task and resource analyses to translate system requirements into resource evaluation and documentation products. www2.acc.af.mil /lg/cons/Lgcu/CATS/2401_PWS.doc   (812 words)

 Analytical Hierarchy Process - Business Intelligence Guide Results for Analytical Hierarchy Process   (Site not responding. Last check: 2007-10-20) Oracle Business Intelligence 10g is the industry's most comprehensive offering designed to address the entire spectrum of analytical requirements including query, reporting, more... Goal.Link ensures goals at all levels in the hierarchy are consistent, and offers guidance on how strategic goals can be met. You can take any function, such as help desk, medical protocols, sales training, etc. and have a means of providing continuous advice to your staff and colleagues, anywhere, plus the ability to monitor performance of your staff and colleagues. biguide.computerworld.com /search/keyword/cwbi/Analytical%20Hierarchy%20Process/Analytical%20Hierarchy%20Process   (1458 words)

 Good sources of information about the AHP Zahedi, F., The analytic hierarchy process - A survey of the method and its applications. Saaty, T., Fundamentals of the analytic hierarchy process. Dolan, J.G. and D.R. Bordley, Involving patients in complex decisions about their care: anapproach using the analytic hierarchy process. www2.newpaltz.edu /~liush/ahp.htm   (90 words)

 Make Complex Business Decisions by the Numbers Integrated into this article are two interactive programs that allow the reader to experiment with the Analytical Hierarchy Process (AHP) decision-making model. The first demonstrates the criterion comparison process; the second allows the reader to select a decision of interest, identify the key variables that impact the decision and use the AHP process as decision input. The Analytic Hierarchy Process (AHP) is a decision analysis method that ranks alternatives based on a number of criteria. gbr.pepperdine.edu /021/ahp.html   (1039 words)

 [No title] The case study offers an example of how QFD and the analytical hierarchy process (AHP) techniques can be used to facilitate a decision facing a company grappling with legacy system obsolescence, including the Year 2000 problem. An approach is presented for applying an Analytical Hierarchy Process (AHP) in Quality Function Deployment to improve the accuracy of priorities and make QFD better fit particular projects. In addition to enhancing the ability of developers to hear the "voices of the customers" more clearly, a more accurate deployment of weights can be accomplished by the consistent use of ratio scales, such as produced by the Analytical Hierarchy Process (AHP) throughout QFD. www.qfdi.org /who_is_qfdi/linkpages/ahp_articles.htm   (524 words)

 MGMT 6100   (Site not responding. Last check: 2007-10-20) The techniques of quantitative business methods we are going to study in this course have been applied successfully to an increasingly wide variety of complex problems in business and industry, health care, education, and many other areas. During the course, you will be introduced to the modern methods and techniques of quantitative decision making: goal and integer programming, analytical hierarchy process, decision tree analysis, inventory models, queuing theory and waiting lines, and simulation. Multiobjective decision making applying the Analytical Hierarchy Process: developing the hierarchy, establishing priorities, pairwise comparison matrix, consistency, and overall priority ranking. www.sbe.csuhayward.edu /~zradovil/6100_fa_2002.htm   (632 words)

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