2. SuperDecisions Software Tutorial
Hyperlinked Index (must be in Slideshow mode for hyperlinks to work)
• Outline of Process
• Create a cluster
• Create a node in a cluster
• Create links between nodes (and hence clusters)
• Make pairwise comparisons: Assess/Compare>node comparisons
• Improving Consistency in making comparisons
• Direct Data Entry
• Building an AHP relative model to choose a car
• The Three Types of Supermatrices
• Getting Results
• Doing Sensitivity Analysis
• Relative vs. Ratings Models
• Building an AHP Ratings model to choose a car
• Moving to Network Models
3. Outline of AHP/ANP
Relative 4. Synthesis-Supermatrix
1. Design unweighted, weighted, limit
– Clusters 5. Sensitivity
– Nodes
1. Links Ratings
– Node to Nodes
1. Design: same as relative,
but alternatives in
1. Judgments spreadsheet, not in hierarchy
(comparisons)
–
2. Spreadsheet: covering
Matrix
criteria; intensity categories
– Verbal for each criterion and scale
– Graphic from comparisons; rating the
– Questionnaire alternatives one at a time
4. Download the file: SuperDecisionsSoftware_v1_6.exe
from the Pitt Courseweb Week 1. Double-click on it to
install it. This icon will appear on your desktop.
Double-click on the icon on your desktop
to run the software. You must enter a
serial number the first time you run it.
This one is valid through December 2007:
WB43-AWVAY-PWPP
6. B
A
E
D C
Validation exercise: Pairwise compare these figures to
determine their relative areas. That is, the percent each
figure has of the area of all the figures put together.
10. Pairwise Comparison Matrix
• We will demonstrate how to use the
software to create a simple pairwise
comparison matrix for comparing three
cars with respect to the property of
prestige.
11. The Cars
• Acura TL
– Cost $30,000-$35,000
– Miles per Gallon 20/29 (City/Hwy)
– Prestige is very good
– Comfort is excellent
• Toyoto Camry
– Cost $22,000 - $28,000
– Miles per gallon 22/30 (City/Hwy)
– Prestige is good
– Comfort is good
• Honda Civic
– Cost $16,000 - $20,000
– Miles per gallon 29/38 (City/Hwy)
– Prestige is medium to low
– Comfort is medium to low
12. Create a Cluster
Select Design>Cluster>New to create cluster
Enter cluster name and description
Save
13. Create a Node in the Cluster
Right-click on cluster background to show
dropdown menu (or use Design>Node command
on main menu)
Enter node name Prestige
Click “Create Node” and description (optional)
Save
14. Cluster with node in it
Add another cluster
with 3 nodes in it
for the
alternatives, the
cars:
1. Acura TL (about
$35,000)
2. Toyoto Camry
(about $30,000)
3. Honda Civic
(about $16,000)
15. Two clusters – not yet connected
Connections icon
close-up view
Click at top
of cluster
and drag to
move it
Left-click around
“connections”
icon to Click on this
depress it button and
and enter drag to resize
“make cluster
connections”
mode Double-click
anywhere on a
cluster to
iconize/expand
16. 2. Links
Link the Prestige node to each of the car nodes
1 Left-click on
“from” or parent
node
Make sure
“connections”
2 Right-click
icon is depressed
successively
on “to” or
children nodes
3 Link then
automatically
appears between
clusters
You can also use the Design>Make Connexions command
to make links!
17. 3. Comparison Judgments
Close-up of
“Compare Left-click on “parent” node then left-
nodes” icon click on “compare nodes” icon
to launch comparison node selector
with Prestige the “wrt” node
Node Comparison
Selector Box
Click here to continue on
into comparison mode
18. Pairwise comparison matrix for cars
with respect to Prestige
Select Misc.>Comparison Words and change
comparison word from “important” to “preferable”
19. Enter pairwise comparisons for
cars with respect to Prestige
DOMINANCE STATEMENT FOR
CURRENTLY SELECTED CELL (Civic vs
Camry)
Blue – left element is
Inconsistency
dominant ratio 0.0515<10%
Red – top element so it is OK
is dominant
Double-click arrow to
invert dominance
Select Computations>Show new
priorities
20. The Comparison Matrix
• The Software View • The Theory View
Acura Civic Camry
Acura 1 8 4
Civic 1/8 1 1/4
Camry 1/3 4 1
Diagonal elements are always 1 and do not
need to be displayed. The crossed out
elements are always inverses of the
Elements in red are actually
judgment in the reciprocal cell and do not
reciprocals. For example, 4.0
need to be displayed.
stands for 1/4
aij = 1/ aji
21. Example
A Three-Level Hierarchy
Goal
Buy Best Car
Price MPG
Prestige (Miles per Comfort
gallon)
Acura TL Toyota Camry Honda Civic
22. Improving Inconsistency
• Inconsistency of < 10% is tolerable. However, the software
can help improve it.
• Inconsistency can be improved only in the Matrix mode
Select Computations>Basic Inconsistency Report
The most inconsistent judgment is listed
first and identified as the AcuraTL versus
Honda Civic judgment of 4. The blue color
indicates row element (Acura) is dominant,
red would indicate column element
dominant. Click on either the Row or
Column name to select the cell in
question. You may type in the suggested
value, a value of your own selection or go
on to the next pair..
23. Inconsistency (cont’d)
• The “best value” suggested for the (Acura,Civic) cell is
1.9988. This value will bring the inconsistency down the
most. Enter it or some other value that best represents
your feeling.
• Entering 1.9988 gives an inconsistency of 0.0000. You do
NOT have to use the suggested number. Choose the
number that best represents your understanding.
• Entering a 3 gives an inconsistency of 0.0176 – still an
improvement on 0.0515.
• If a number less than 1.0 is suggested, type the fraction in
the appropriate cell. The software will automatically
convert a fraction to a “red” number greater than 1.0 . It
means the column element is dominant and the arrow
points up. In the AHP literature this would be an inverse
number with .33 would be a 1/3.
24. 3 Other Comparison Modes
Graphic Verbal
Tracking
– shows
which
judgment
you are on
Questionnaire Click to invert
Click and dominance
drag on
circle to
change
judgment
25. Other Comparison Mode Features
Miscellaneous Command
•Direct data entry – enter
priorities or data directly
•Comparison words –
select Importance,
Preference, Likelihood, or
enter your own word
•Restore Initial Values –
restore values that were
there upon entering the
comparison mode
Close Comparison Mode
Judgments automatically
save upon closing
•Select File>Save and Close
•Or click on
26. Miscellaneous Comparison
Commands
– Direct Data Entry
(select Inverted button to invert
Priorities when large numbers
are undesirable. Use for costs,
for example, where larger
numbers should have smaller
Priorities.)
– Comparison Words
(Select best word to describe
type of comparison or enter your
own comparison word)
27. Direct Data
• To directly input values select Direct Data in the
comparison mode; for example to input dollars
or some other measures. The values will be
normalized to give the priorities.
• Inconsistency is always zero for direct data
Invert if
cheaper is Honda gets
preferred – highest priority
usually the
case with
28. Weaknesses of using Direct Data
• Data may not be as good as judgments in determining your personal
priorities. It would usually be better to prioritize the price of the cars
to customize the priorities for you instead of using the data directly.
Suppose you are a poor college student. See the two results below.
Which do you think more accurately reflects the reality?
Comparing cars for price using
judgments
Priorities from Priorities
judgments from data
29. To Build a 3-level Hierarchy
Step 1. Create the clusters and nodes shown below
Connections icon
close-up view
Click this
button and
drag to re-
Turn on “Make size cluster
Connections”
mode by left- Name clusters
clicking and nodes
“connections” with number
icon. prefixes. The
supermatrix is
arranged
alphabetically
so numbering
controls order
of presentation
in supermatrix
30. Make Connections or Links from Goal Node
to Criteria Nodes
1 2
Left-click “from” node
Make sure (depresses node)
“Make
connections”
icon is on 3
(depressed) Right-click
each “to” node
4
Line will
automatically
appear from
Goal cluster to
Criteria cluster
31. Connect Criteria Nodes to
Alternative Nodes
SHORTCUT
to connect
many nodes
at once
Shift left-click on any
“from” node selects all
Shift right-click
on any “to” node
connects all to all
Again, line automatically appears between clusters
32. Showing Node Connections
Close-up of “show
connections icon
Hold cursor over
any node and all
nodes it
Left-click on connects “to”
“show will be outlined
connections” in red.
icon to
depress it.
34. Pairwise Compare Criteria with
respect to the Goal
1. Left-click on Goal node to select it
2. Left-click on “node comparisons” icon
Node comparison selector box will appear
Matrix mode for making comparisons
3. Left-click “Do Comparisons” button to
get into the Comparisons mode and
click on Matrix to bring up the matrix
view.
4. The (Prestige, Price) cell is highlighted
so it is the current judgment
35. Enter pairwise comparisons for
criteria with respect to the goal
Enter judgments from AHP 1-9 scale
(MPG, Comfort) is current judgment
Blue – left element
is
dominant
Red – top element
is dominant
Double-click
Inconsistency index is 0.0768.
arrow to invert (it is less than 0.10 so it is
dominance
okay)
Select “Computations/Show New Priorities”
Resulting
Priorities
36. To Show Completed Comparisons
Always mark comparisons complete as you finish
them and are back in the node selector box. Turn on “Show Connections” icon and
hold cursor over “parent” node to
show its “children” nodes outlined in
red. The entire cluster will be outlined
in red when comparisons have been
marked complete.
38. Compare Cars for Prestige and Price
Prestige Comparisons and Priorities
Price Comparisons and Priorities
39. Compare Cars for MPG and Comfort
MPG Comparisons and Priorities
Comfort Comparisons and Priorities
40. 4. Synthesis
The Supermatrices
1. Computations>Unweighted Supermatrix: matrix
containing the priorities from the pairwise
comparisons.
2. Computations>Weighted Supermatrix: The
unweighted supermatrix components have been
multiplied by cluster weights. In a hierarchy the
weighted supermatrix is the same as the
unweighted.
3. Computations>Limit Supermatrix: Limit matrix is
obtained by raising weighted supermatrix to
powers until it converges to give the answer.
42. Results
• Select Computations>Synthesize or click to get
the final results: the priorities of the alternatives.
Acura TL 0.344
Toyota Camry 0.200
Honda Civic 0.456
The Raw values come from
the Limit Supermatrix. The
Normalized values are
obtained from them by
normalizing. The Ideals are
obtained by dividing all Raw
values by the largest of them.
44. 5. Sensitivity Analysis
1. Select Computations>Sensitivity
command
2. Edit>Independent Variable in
order to change the Independent
Variable to the Goal.
3. In the Selected Node box highlight
the current node and click Edit.
4. In the Input Parameter Box select
Parameter Type: Supermatrix,
Goal as wrt Node, and one of the
criteria as the First Other Node,
for example, Prestige.
5. Click Done and Update to see the
sensitivity graph for that criterion.
The first graph that appears is
generally not the one you want.
You want the Goal, not the
Acura TL, as the independent
variable
45. Getting Sensitivity Graph for Prestige
Show Selected Node Box Set Parameters Box
1 2
Sensitivity Graph for Selected node(s)
Show Selected Node Box
Priority of Prestige
is given on x-axis;
vertical line is at
Prestige priority of
3 4 50%; car priorities
for Prestige=50%
priority are shown
by intersections
with vertical line.
46. Priorities of all Nodes in Model
• Select Computations>Priorities
command to see priorities of all
nodes in model
• “Limiting priority” column shows
value of Prestige from Limit
supermatrix (.049)
• “Normalized by Cluster” column
shows overall priority of Prestige
(.096) in model.
• Drag the vertical line from .5 to .
096 on the x-axis in Sensitivity to
show the priorities of the cars at
that priority for Prestige.
47. Change Priority of Prestige
At Prestige = 50%, Acura is best At Prestige = 9.2% (actual value), Civic is
best
Click and drag vertical line to change priority of Prestige
The analysis: If your priority is less than about 25% for Prestige, the Honda is the car
to buy. For any priority greater than that, the Acura is your best car.
48. Subcriteria in a Hierarchical Model
• One creates clusters
for the subcriteria.
• Price connects to its
subcriteria, initial cost
and maintenance,
which then connect to
the cars
• Comfort connects to
its subcriteria Ride
and Driving
Performance which
then connect to the
cars.
• Prestige and MPG
connect directly to the
cars as they have no
subcriteria.
49. Ratings
• Relative models: In a relative model such
as the car model all nodes are pairwise
compared to establish priorities.
• Ratings models: In a ratings model
standards are established for the criteria
and the alternatives are rated one at a
time against them.
50. Create a Ratings Model
1. Build a hierarchical model as shown below and enter judgments as before, but do not
include the alternatives in the main screen of the model. The model has 4 criteria and the
Comfort criterion has subcriteria of Ride and Driving Performance.
2. Select Design>Ratings to open the Ratings screen where the Alternatives will be evaluated.
51. Starting Ratings
1. Blank screen appears
2. Select Edit Criteria New and click on the criteria/subcriteria to appear as column headings.
You must start by adding Criteria (trying to add Alternatives first will result in a software
crash at present). Select the lowest level of covering criteria. Do NOT select Comfort;
instead select its subcriteria, Driving Performance and Ride.
52. Ratings Spreadsheet
3. Ratings spreadsheet now has selected criteria in it as shown below:
4. Select Edit>Alternatives>New and enter name for each alternative:
5. The Ratings Spreadsheet now has one alternative; continue adding alternatives:
53. Ratings Spreadsheet (cont’d)
5. Ratings Spreadsheet in which alternatives have been entered
6. Select Edit>Criteria> Edit Categories from menu or right-click on a column heading, for
example, Prestige, to get the dropdown menu and select Edit Categories.
54. Ratings Spreadsheet (cont’d)
7. Category Editor will appear. Enter names of Categories for the Prestige criterion (use New command)
8. Click Comparisons in Category Editor to bring up pairwise comparison screen
a. Change comparison word to
“preferred”
b. Enter judgments –
questionnaire mode appears
but you can use any mode.
c. Improve inconsistency to less
than 0.10
55. Ratings Spreadsheet (cont’d)
9. Compute priorities with Computations>Ideal Priorities command.
The Ideal priorities are computed from the usual Priorities by dividing
each priority by the largest.
8. Close the Comparisons screen in the
usual way to return to the Ratings
Spreadsheet. The categories have
been established and pairwise
compared for Prestige.
9. Click on the (Acura, Prestige) cell to
show the categories from which you will
choose the applicable rating and
choose Excellent.
56. Ratings Spreadsheet (cont’d)
10. Repeat the process to create the categories for Price and prioritize.
Note that we have made the Price categories ranges of prices and that the
lowest price range is the most preferred and gets the highest priority.
11. To display the priorities associated with
the categories as shown here, turn on
View>Category Display>Names and
Priorities
12. Click on the (Acura, Price) cell and
select its price range which has a
priority of .085.
57. Ratings Spreadsheet (cont’d)
13. Create categories for the remaining columns and rate the alternatives
14. Display Totals and Priorities columns with the View command
58. Results in Ratings
15. Final rated spreadsheet. The Priorities are the results.
16. Priorities can also be displayed with the Calculations>Synthesize command
Ratings Relative Model
Acura TL .280 .344
Toyota Camry .264 .200
Honda Civic .456 .455
60. Network Models do not have
Goals
A network model has a
criteria cluster and an
alternatives cluster, but
no goal.
The alternatives are
prioritized for each
criterion as in an AHP
model.
61. Establishing Priorities for Criteria
In AHP criteria are prioritized by
answering the question, “How important
is C1 compared to C2 with respect to the
goal?” Sometimes too abstract a question to answer.
In ANP criteria are prioritized by asking
how important they are in each of the
alternatives being considered. Usually an easier
question to answer when looking at actual alternatives that
have the properties in question.
62. Criterion Prestige connected to
Alternative Cars and Cars Prioritized
(and similarly for the other criteria)
.707
.070
.223
63. Feedback: Link Alternatives to Criteria and
compare for Preference
For example, a pairwise question would be: “For the Acura TL, which do
you like better, its prestige or its price?” ; “Its prestige or its MPG?” etc.
.499
.066
.079
.355
65. Make Comparisons
For each of the 3 cars compare your
preference for their properties (or
criteria) of Prestige, Price, MPG, and
Comfort (same as in a hierarchy)
This results in the three vectors of
priorities for the criteria that go into the
supermatrix. From these the limit
supermatrix will net out an overall
vector of priorities for the criteria.
66. Pairwise Compare Criteria for each Car
Acura TL Results for Acura TL
Results for Toyota Camry
Toyota Camry
68. The Unweighted Supermatrix
For example, the priorities in the last column come from
comparing the criteria with respect to the Honda Civic. That
is, what we value most about the Honda is its price.
69. Limit Supermatrix
The limit supermatrix is obtained by raising the weighted supermatrix to powers
until it converges (in this case all columns are the same, though not always true).
The final answer, the
synthesis, below is
obtained by normalizing
the raw values for the
alternatives from the limit
supermatrix:
ANP AHP
Acura TL .457 .344
Toyota Camry .173 .200
Honda Civic .369 .455
70. Why are the results different?
•In AHP – the user, going top-down making
comparisons, when asked without referring
to actual alternatives, over-estimated the
importance of cost.
•In ANP – the user learned through
feedback comparisons that his/her priority
for Cost is not nearly as high as originally
thought when asked the question abstractly,
while Prestige gets more weight.
This is why a husband and wife, setting out to the dealership to buy a “sensible” low
priced car, walked out with something entirely different and much more costly.
When they saw the shiny cars on the showroom floor they revised their priorities.
71. Inner and Outer Dependence
•Outer dependence - the parent node and
the nodes to be compared are in different
clusters. A directed link appears from the
parent node cluster to the other cluster.
•Inner dependence - the parent node and
the nodes to be compared are in the same
cluster. The cluster is linked to itself and a
loop link appears.
72. We can add some inner dependence: eg, price
is influenced by prestige and comfort; and
prestige is influenced by price and comfort.
73. An Example of an Inner Dependent
Comparison is shown below:
Which influences Price more, Prestige or Comfort?
Which influences Prestige more, Price or Comfort?
74. The results with the interdependencies in
place are:
ANP ANP AHP
(With dependencies)
Acura TL .487 .457 .344
Toyota Camry .182 .173 .200
Honda Civic .331 .369 .455
