The Analytic Hierarchy Process and SDSS

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The Analytic Hierarchy Process and SDSS

• RNR/GEOG 420-520

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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)

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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

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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.

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Types of Decisions
Most decisions are semi-structured, where only
part of the problem has a clear-cut answer
provided by a well-defined procedure
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A Decision Support System

• It is an information system (not necessarily a
  computer system) that combines data, analytical
  tools and models to support semi-structured and
  unstructured decision making
• It is not a decision maker

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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

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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.
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Components of Group DSS

• Database
• Model base
• Analysis System
• Dialogue manager
• Communication capability
• Special software (also called GroupWare)

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Group DSS Equipment
Decision Room For decision makers located in the
same geographic area or building. Use of
computing devices, special software, networking
capabilities, display equipment, and a session
leader to collect, coordinate, and feed back
organized information to help a group make a
decision.
Database Model base Dialogue manager Communication
capability Special software (also called
GroupWare)
Combines face-to-face verbal interaction with
technology-aided formalization.
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Or

• Wide Area 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.

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Spatial Decision Support System

• SDSS add the element of location
• Lots of different applications for SDSS
• Almost all of them involve GIS

Spatial decision-making select from spatially
distributed options
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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
• i.e. maps/displays as means of visualising the
  problem
• overlays as means of defining relationships
• modelling as means of predicting outcomes
• Etc.

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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

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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.
  (www.expertchoice.com)

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The AHP Process
Remember, it is more important to know the AHP
process than the AHP math for the exam!

• State the goal
• Define the criteria (variables)
• Identify the alternatives (choices)
• Arrange information in a hierarchical tree
• Make pairwise comparisons
• Construct matrix of comparisons
• Calculate priorities (eigenvectors)

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Example situating a landfill

• State the Goal
• Select site for landfill
• Define the Criteria (or Variables)
• Area (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 Wisslers house

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Pairwise Alternatives and Variables
Locate a Landfill
Objective
Distance to Drainage
Area
Visibility
Criteria
Craigs House
Site 3
Site 2
Site 1
Alternatives
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Make Pairwise Comparisons

• Area is 2 times more important than Drainage
• Drainage is 3 times more important than
  Visibility
• Area is 4 times more important than Visibility

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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. 0.00001)

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Matrix Mathematics

• Original matrix
• Squared (matrix algebra)

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More Matrix Mathematics
12.750
Row Totals
22.333
4.833
39.9165
12.750/39.9165 0.3194
Priorities (eigenvector)
22.333/39.9165 0.5595
4.833/39.9165 0.1211
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Results

• Repeat until differences in the priorities are
  zero to the ten-thousandths position
• Area 0.5595 (Most important)
• Drainage 0.3194 (Second most important)
• Visibility 0.1211 (Least important)

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Pairwise Alternatives and Variables
Locate a Landfill
Objective
Distance to Drainage
Area
Visibility
Criteria
Craigs House
Site 3
Site 2
Site 1
Alternatives
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How Does This Provide an Answer?
First, AHP does pairwise comparisons between the
alternatives for each of the criteria/variables
Craigs
Site 1
Area Visibility Drainage
Area Visibility Drainage
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What About AHP and SDSS?
Find a LocationFor Lagomorphismillepidis
Objective
Area
New Fencing
Vegetation Patchiness
Criteria/ Variables
Site D
Site C
Site B
Site A
Alternatives
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What Happens When there are Thousands of
Alternatives?
Find a LocationFor Lagomorphismillepidis
Objective
New Fencing
Area
Vegetation
Criteria/ Variables
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When There are Too Many Alternatives
Find a LocationFor Lagomorphismillepidis
And you have ratio scale data
Area
Instead of doing pairwise comparisons between
alternatives, use the variable scores to weight
the alternatives
New Fencing
Vegetation
Site D
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