TUTORIALThe SuperDecisions Software for AHP and ANP
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
Outline of AHP/ANP Relative 4. Synthesis-Supermatrix1. Design unweighted, weighted, limit – Clusters 5. Sensitivity – Nodes1. Links Ratings – Node to Nodes 1. Design: same as relative, but alternatives in1. 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
Download the file: SuperDecisionsSoftware_v1_6.exefrom the Pitt Courseweb Week 1. Double-click on it toinstall 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
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.
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
Create a ClusterSelect Design>Cluster>New to create cluster Enter cluster name and description Save
Create a Node in the ClusterRight-click on cluster background to showdropdown menu (or use Design>Node commandon main menu) Enter node name Prestige Click “Create Node” and description (optional) Save
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)
Two clusters – not yet connectedConnections icon close-up view Click at top of cluster and drag to move itLeft-click around“connections”icon to Click on thisdepress it button andand enter drag to resize“make clusterconnections”mode Double-click anywhere on a cluster to iconize/expand
2. Links Link the Prestige node to each of the car nodes 1 Left-click on “from” or parent nodeMake sure“connections” 2 Right-clickicon 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!
3. Comparison JudgmentsClose-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
Pairwise comparison matrix for cars with respect to Prestige Select Misc.>Comparison Words and change comparison word from “important” to “preferable”
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 dominanceSelect Computations>Show newpriorities
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
ExampleA Three-Level Hierarchy Goal Buy Best Car Price MPGPrestige (Miles per Comfort gallon) Acura TL Toyota Camry Honda Civic
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..
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.
3 Other Comparison Modes Graphic Verbal Tracking – shows which judgment you are on Questionnaire Click to invertClick and dominancedrag oncircle tochangejudgment
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
Miscellaneous Comparison Commands– Direct Data Entry(select Inverted button to invertPriorities when large numbersare undesirable. Use for costs,for example, where largernumbers should have smallerPriorities.)– Comparison Words(Select best word to describetype of comparison or enter yourown comparison word)
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
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 usingjudgments Priorities from Priorities judgments from data
To Build a 3-level Hierarchy Step 1. Create the clusters and nodes shown belowConnections icon close-up view Click this button and drag to re-Turn on “Make size clusterConnections”mode by left- Name clustersclicking and nodes“connections” with numbericon. prefixes. The supermatrix is arranged alphabetically so numbering controls order of presentation in supermatrix
Make Connections or Links from Goal Node to Criteria Nodes 1 2 Left-click “from” nodeMake sure (depresses node)“Makeconnections”icon is on 3(depressed) Right-click each “to” node 4 Line will automatically appear from Goal cluster to Criteria cluster
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
Showing Node ConnectionsClose-up of “showconnections 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.
Supermatrix before making pairwise comparisons
Pairwise Compare Criteria with respect to the Goal1. Left-click on Goal node to select it2. 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
Enter pairwise comparisons forcriteria 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
To Show Completed ComparisonsAlways mark comparisons complete as you finishthem 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.
SuperMatrix showing Priorities ofCriteria with respect to the Goal
Compare Cars for Prestige and Price Prestige Comparisons and Priorities Price Comparisons and Priorities
Compare Cars for MPG and Comfort MPG Comparisons and Priorities Comfort Comparisons and Priorities
4. Synthesis The Supermatrices1. 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.
The Unweighted Supermatrixafter all Judgments Completed
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.
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
Getting Sensitivity Graph for Prestige Show Selected Node Box Set Parameters Box1 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 of3 4 50%; car priorities for Prestige=50% priority are shown by intersections with vertical line.
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.
Change Priority of PrestigeAt 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.
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.
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.
Create a Ratings Model1. 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.
Starting Ratings 1. Blank screen appears2. 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.
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:
Ratings Spreadsheet (cont’d)5. Ratings Spreadsheet in which alternatives have been entered6. Select Edit>Criteria> Edit Categories from menu or right-click on a column heading, forexample, Prestige, to get the dropdown menu and select Edit Categories.
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
Ratings Spreadsheet (cont’d)9. Compute priorities with Computations>Ideal Priorities command.The Ideal priorities are computed from the usual Priorities by dividingeach 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.
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 thelowest 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 Priorities12. Click on the (Acura, Price) cell and select its price range which has a priority of .085.
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
Results in Ratings15. 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
Changing from a Hierarchical Model to a Network Model
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.
Establishing Priorities for Criteria In AHP criteria are prioritized byanswering the question, “How importantis C1 compared to C2 with respect to thegoal?” Sometimes too abstract a question to answer. In ANP criteria are prioritized by askinghow important they are in each of thealternatives being considered. Usually an easierquestion to answer when looking at actual alternatives thathave the properties in question.
Criterion Prestige connected toAlternative Cars and Cars Prioritized (and similarly for the other criteria) .707 .070 .223
Feedback: Link Alternatives to Criteria and compare for PreferenceFor example, a pairwise question would be: “For the Acura TL, which doyou like better, its prestige or its price?” ; “Its prestige or its MPG?” etc. .499 .066 .079 .355
Make Comparisons For each of the 3 cars compare yourpreference for their properties (orcriteria) of Prestige, Price, MPG, andComfort (same as in a hierarchy)This results in the three vectors ofpriorities for the criteria that go into thesupermatrix. From these the limitsupermatrix will net out an overallvector of priorities for the criteria.
Pairwise Compare Criteria for each Car Acura TL Results for Acura TL Results for Toyota Camry Toyota Camry
The Unweighted SupermatrixFor example, the priorities in the last column come fromcomparing the criteria with respect to the Honda Civic. Thatis, what we value most about the Honda is its price.
Limit SupermatrixThe limit supermatrix is obtained by raising the weighted supermatrix to powersuntil 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
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” lowpriced 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.
Inner and Outer Dependence•Outer dependence - the parent node andthe nodes to be compared are in differentclusters. A directed link appears from theparent node cluster to the other cluster.•Inner dependence - the parent node andthe nodes to be compared are in the samecluster. The cluster is linked to itself and aloop link appears.
We can add some inner dependence: eg, priceis influenced by prestige and comfort; andprestige is influenced by price and comfort.
An Example of an Inner DependentComparison is shown below: Which influences Price more, Prestige or Comfort? Which influences Prestige more, Price or Comfort?
The results with the interdependencies inplace are: ANP ANP AHP (With dependencies) Acura TL .487 .457 .344 Toyota Camry .182 .173 .200 Honda Civic .331 .369 .455