The Analytic Hierarchy Process and SDSS

Transcription

1 The Analytic Hierarchy Process and SDSS RNR/GEOG Preview Week 12 Spatial Decision Support Systems (SDSS) and the Analytic Hierarchy Process (AHP) Week 13 Designing Geodatabase Models Week 14 GeoVisualization and Pseudo 3D models Week 15 Internet Map Services (IMS) 1

2 Grad Student Study Plans Have you all picked a topic? Have you talked to Craig or I about this topic? These are due April 25 that s 2 weeks from today Overview of SDSS and AHP The Basics: Decision Making & Problem Solving Decision Support Systems Spatial Decision Support Systems The element of location The relationship to GIS GIS and Group decision making The Analytic Hierarchy Process AHP and GIS, a Group SDSS An example of AHP and GIS in an SDSS 2

3 Problem Solving and Decision Making Decision making Intelligence: identify and define potential problems and/or opportunities. Design: develop alternative solutions to the problem. Choice: select a course of action. Problem solving Implementation: take action to put the solution into effect. Monitoring: evaluate the implementation of the solution. Types of Decisions Structured decisions use a rule, procedure, or quantitative method Structured Unstructured decisions deal with unusual or exceptional situations Unstructured Most decisions are semistructured, where only part of the problem has a clear-cut answer provided by a welldefined procedure 6 3

4 A Decision Support System It is an information system (not necessarily a computer system) that combines data, analytical tools and models to support semistructured and unstructured decision making Structured Unstructured It is not a decision maker Components of a DSS Information System Access to internal and external databases Model System Access to a variety of simulation and/or decision making models Analysis System Uses data and models to answer questions User Interface User-friendly access to the above systems 4

5 Group Decision Support Systems Group Decision Support System (GDSS) Contains most of the elements of DSS plus software to provide effective support in group decision-making settings. Components of Group DSS Database Model base Analysis System Dialogue manager Communication capability Special software (also called GroupWare) 5

6 Group DSS Equipment Decision Room For decision makers located in the same geographic area or building. Use of computing devices, Database special software, networking capabilities, Model base display equipment, and Dialogue a session manager leader to collect, coordinate, Communication and capability feed back organized information Special software to (also called GroupWare) help a group make a decision. Combines face-to-face verbal interaction with technology-aided formalization. Or Wide Decision Network Location of group members is distant. Decision frequency is high Virtual workgroups Groups of workers located around the world working on common problems via a GDSS. 6

7 Spatial Decision Support System SDSS add the element of location Lots of different applications for SDSS Spatial decision-making: select from spatially distributed options Almost all of them involve GIS SDSS and GIS GIS is a natural component of SDSS GIS is not an SDSS GIS can provide certain tools for assisting in the decision making process, e.g. a spatial database maps/displays as means of visualising a problem overlays as means of defining relationships between layers modelling as means of predicting outcomes etc. 7

8 Components of SDSS Information System Access to internal and external databases Model System Access to a variety of decision making models Spatial System Access to a variety of spatial data Analysis System Uses information, models, and spatial data to answer questions User Interface User-friendly access to the above systems An Example Analytic Hierarchy Process (AHP) The Analytic Hierarchy Process (AHP) is a powerful and flexible decision making process to help people set priorities and make the best decision when both qualitative and quantitative aspects of a decision need to be considered. By reducing complex decisions to a series of one-on-one comparisons, then synthesizing the results, AHP not only helps decision makers arrive at the best decision, but also provides a clear rationale that it is the best. ( 8

9 The AHP Process State the goal Define the criteria (variables) Identify the alternatives (choices/solutions) Arrange information in a hierarchical tree Make pairwise comparisons Construct matrix of comparisons Calculate priorities (eigenvectors) Remember, it is more important to know the AHP process than the AHP math for the exam! Example: situating a landfill State the Goal Select site for landfill Define the Criteria (or Variables) (we need enough space for all the trash) Visibility (we need a location that nobody can see) Drainage (we need a location far from major drainages) Identify the Alternatives (or Choices) Site 1 Site 2 Site 3 Craig Wissler s house 9

10 Hierarchical Arrangement Pairwise Comparison Alternatives and Variables Objective Locate a Landfill Distance to Drainage Criteria Visibility Alternatives Site 1 Site 2 Site 3 Craig s House Make Pairwise Comparisons is 2 times more important than Drainage Drainage is 3 times more important than Visibility is 4 times more important than Visibility Drainage Visibility Drainage Visibility

11 To Calculate Priorities Square the matrix The row sums are then calculated and normalized This results in an approximation of the eigenvector Stop when the difference between the values in two consecutive calculations is smaller than a prescribed value (e.g ) Matrix Mathematics Original matrix Squared (matrix algebra)

12 More Matrix Mathematics = = = Row Totals / = / = / = Priorities (eigenvector) Results Repeat until differences in the priorities are zero to the ten-thousandths position : (Most important) Drainage: (Second most important) Visibility: (Least important) 12

13 Pairwise Alternatives and Variables Objective Locate a Landfill Distance to Drainage Criteria Visibility Alternatives Site 1 Site 2 Site 3 Craig s House How Does This Provide an Answer? First, AHP does pairwise comparisons between the alternatives for each of the criteria/variables Visibility Drainage Craig s Site Visibility Drainage Based on these comparisons, it scores and ranks the alternatives Craig s.45 Site 1.35 Site 3.15 Site

14 What About AHP and SDSS? Objective Find a Location For Lagomorphis millepidis Criteria/ Variables Vegetation Patchiness New Fencing Alternatives What Happens When there are Thousands of Alternatives? Objective Find a Location For Lagomorphis millepidis Criteria/ Variables Vegetation New Fencing Alternatives Site Site Site Site Site A Site B Site C Site D Site Site Site Site A A B B C C Site Site 101,002 DD D Site 100,999 Site 101,000 Site 101,001 14

15 When There are Too Many Alternatives And you have ratio scale data Find a Location For Lagomorphis millepidis Instead of doing pairwise comparisons between alternatives, use the variable scores to weight the alternatives Vegetation New Fencing Site Site Site Site Site A Site B Site C Site D Site Site Site Site A A B B C C Site Site 101,002 DD D Site 100,999 Site 101,000 Site 101,001 15