The Analytic Hierarchy
Process and SDSS
RNR/GEOG 420-520
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
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Have you talked to Craig or I about this topic?
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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
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
Unstructured decisions
deal with unusual or
exceptional situations
Most decisions are
semi-structured, where only part of
the problem has a clear-cut
answer provided by a
well-defined procedure
It is an information system (not necessarily a
computer system) that combines data,
analytical tools and models to support
semi-structured and unsemi-structured decision making
It is not a decision maker
A Decision Support System
Structured
Unstructured
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
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
Group DSS Equipment
Database
Model base
Dialogue manager
Communication capability
Special software (also called GroupWare)
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.
Combines face-to-face verbal interaction
with technology-aided formalization.
Or …
Wide Area Decision Network
z
Location of group members is distant.
zDecision frequency is high
z
Virtual workgroups
Groups of workers located around
the world working on common
problems via a GDSS.
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
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
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.
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)
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
Hierarchical Arrangement
Pairwise Comparison
– Alternatives and Variables
Locate a Landfill Craig’s House Site 3 Site 2 Site 1Objective
Alternatives
Criteria
Area Distance to Drainage VisibilityMake 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
1
0.25
0.333
Visibility
4
1
2
Area
3
0.5
1
Drainage
Visibility
Area
Drainage
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)
Matrix Mathematics
1.000
0.250
0.333
4.000
1.000
2.000
3.000
0.500
1.000
3.000
0.667
1.167
14.000
3.000
5.333
8.000
1.750
3.000
Original matrix
More Matrix Mathematics
3.000
0.667
1.167
14.000
3.000
5.333
8.000
1.750
3.000
= 12.750
= 22.333
= 4.833
Row
Totals
12.750/39.9165 = 0.3194
22.333/39.9165 = 0.5595
4.833/39.9165 = 0.1211
39.9165
Priorities
(eigenvector)
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)
Pairwise – Alternatives and Variables
Locate a Landfill Craig’s House Site 3 Site 2 Site 1Objective
Alternatives
Criteria
Area Distance to Drainage VisibilityHow Does This Provide an Answer?
0.623 0.138 0.239 0.155 0.069 0.777
Area
Visibility
Drainage
Craig’s
Site 1
Area
Visibility
Drainage
First, AHP does pairwise comparisons between
the alternatives for each of the criteria/variables
Craig’s
Site 1
Site 3
Site 2
.05
.15
.35
.45
Based on these
comparisons, it scores
and ranks the alternatives
What About AHP and SDSS?
Find a Location For Lagomorphis millepidis New Fencing Area Vegetation Patchiness Site D Site C Site B Site AObjective
Alternatives
Criteria/
Variables
What Happens When there are Thousands
of Alternatives?
Find a Location For Lagomorphis millepidis New Fencing Area Vegetation Site D Site C Site B Site AObjective
Alternatives
Criteria/
Variables
Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site BSite ASite A Site B Site C Site D Site D Site C
Site B
Site ASite A Site B Site C Site D Site D Site C
Site B
Site ASite A Site B Site C Site D Site D Site C
Site B
Site ASite A Site BSite B Site CSite C Site DSite D Site A Site BSite BSite B Site CSite CSite C Site DSite DSite D Site ASite A Site B Site C Site D
Site D Site C Site B Site A Site D Site C Site B
Site A Site B Site C Site D
Site A Site B Site C Site D
Site ASite A Site B Site C Site D Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site B
Site A Site B Site C Site D
Site A Site B Site C Site D
Site A Site B Site C Site D
Site ASite A Site B Site C Site D Site D Site C Site B Site A Site D Site C
Site B Site C Site D
When There are Too Many Alternatives
…
Find a Location For Lagomorphis millepidis New Fencing Area Vegetation Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site BSite ASite A Site B Site C Site D Site D Site C
Site B
Site ASite A Site B Site C Site D Site D Site C
Site B
Site ASite A Site B Site C Site D Site D Site C
Site B
Site ASite A Site BSite B Site CSite C Site DSite D Site ASite A Site BSite B Site CSite C Site DSite D Site A
Site D Site C
Site B
Site ASite A Site B Site C Site D Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site B
Site A Site B Site C Site D
Site ASite ASite A Site BSite B Site CSite C Site DSite D Site D Site C Site B Site A Site D Site C Site B Site A Site D Site C Site B
Site A Site B Site C Site D
Site A
Site D Site C
Site B
Site A Site B Site C Site D
Site ASite A Site B Site C Site D Site D Site C Site B Site A Site D Site C Site B
Site A Site B Site C Site D
Site A Site 101,000 Site 101,001 Site 101,002 Site 100,999