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# Tutorial 1 ahp_relative_model_ver_2.2.x

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### Tutorial 1 ahp_relative_model_ver_2.2.x

1. 1. SuperDecisions Software Tutorial• Installing the SuperDecisions Software• Glossary (3 slides)• Building the decision hierarchy• Removing unintended loops• Making Pairwise Comparisons• Improving Consistency of pairwise comparisons• Entering Direct Data instead of Pairwise Comparing• The Three Types of Supermatrices• Getting Results• Sanity Check• Graphical Sensitivity• Dynamic Sensitivity• Restoring backups• Exporting Supermatrices for use in Excel or Word• Reports
2. 2. GlossaryAlternative– an alternative is a node representing one of the choices or outcomes for a decision model. The alternatives are grouped together in a single cluster.Cluster – a cluster is a collection of nodes that have some logical relationship together in a frame inside a SuperDecisions Window.Comparison Group – consists of a parent node linked to a group of children nodes that will be pairwise compared with respect to the parent node for importance, preference or likelihood. The children nodes must be in a cluster together; the parent node may be in a different cluster or in the same cluster as its children nodes, and may have children groups in several clusters.Criterion – a criterion (always use this word when you mean just one!) is a decision factor, something that must be considered when making a decision. A criterion is represented by a node in a SuperDecisions model.Goal – a goal in a model is a single node in a cluster with links only “from” it. In hierarchical models there should be only one goal. In hierarchies criteria nodes are linked from the goal and judgments are made about their importance with respect to the goal. In ANP subnetworks the goal is not an explicit node but is external to the network, often being represented by the name of the network, and is the concept kept in mind while making all judgments on nodes in the network.Hierarchy– In a hierarchy the goal is at the top, the criteria are in a separate cluster connected from the goal, the subcriteria are in clusters connected from a parent criterion. Clusters are often arranged hierarchically with the goal cluster at the top of the window, the criteria cluster below that, the subcriteria clusters below that and the alternative cluster at the bottom.Inconsistency– if element A is preferred to element B by 2 and element B is preferred to element C by 3, then element A should be preferred to element C by their product, 6. If it is not 6, then there is inconsistency. All such triples of judgments for a comparison group are checked for consistency and SuperDecisions gives a measure of the inconsistency as a decimal number that should be less than about 0.10.
3. 3. Glossary (Cont’d)Judgments – a dominance judgment is entered for each pair of children nodes in a comparison group using the Fundamental Scale: 1-Equal, 3-Moderate, 5-Strong, 7- Very Strong, 9-Extremely Strong, plus numbers in between for intermediate judgments, as well as decimals for finer distinction. The judgment modes in SuperDecisions are: Graphical – use ratios of bars or relative areas in a circle Verbal– use a continuous sliding scale on which the words from the Fundamental Scale are indicated Matrix– enter the dominance judgments as numbers in a table or matrix for each pair Questionnaire–use a questionnaire form in which the appropriate whole number from the Fundamental Scale is selected to indicate dominance for each pair Direct–this mode allows the direct entry of priorities for a group of children nodes; numbers which do not add up to 1.0 can also be entered and they will be normalized to give the prioritiesLink or Connection – a link goes from one node to another. A node most often has links to several other nodes.Model– a SuperDecisions model may be a simple network contained in a single window, or a complex model of 2 or 3 or more levels consisting of a main network (window) with attached sub-networks (windows) linked together.Network – any collection of clusters, nodes, and their connections in a single window (a window is a box or frame). A network may be either a hierarchy or a feedback structure.
4. 4. Glossary (Cont’d)Node – a node is an element or factor in a decision such as the goal, a criterion, a subcriterion, or an alternative. Nodes are smaller rectangular frames inside a cluster frame.Normalization– mathematical procedure of summing a group of numbers and dividing each by the sum so that the resulting numbers will sum to 1; the numbers are then said to be normalized to 1. Priorities are sets of numbers normalized to 1. To obtain priorities from any group of numbers apply the procedure above.Priority – Priorities result from making a set of pairwise comparison judgments on a group of children nodes. The priorities sum to 1.Sensitivity– To perform sensitivity with respect to a criterion in a hierarchy means to vary the priority of that node, maintaining the same relative proportion of the other nodes with respect to the goal, and see how the outcome changes. To perform sensitivity in a network is a more complicated process because every node may be involved in many different comparison groups, but it still means to vary the priority of a given element in the structure and see how the outcome changes.Supermatrix – the judgment data for a model is stored in supermatrices (think of an Excel spreadsheet).Synthesis – after judgments are made the model is synthesized to give the best alternative; that is, the one with the highest synthesized priority.Window– a box or frame, sometimes with a menu of commands across the top, or sometimes not, in which case it is called a dialogue box. The opening screen of SuperDecisions is a blank window.
5. 5. SuperDecisions’ Opening Screen Main Menu Commands • File – Open file, Close file, Recent Files, Backups, Export supermatrices, Print preview for text version of model Each model is contained in a separate file. Old files have .mod extensions, new files have .sdmod extensions • Design – Build a network by creating clusters and nodes and making node connections • Assess/Compare – Perform pairwise comparisons, access the Ratings spreadsheet if there is one • Computations – Synthesize results, look at supermatrices, perform sensitivity, do sanity check for errors and incomplete comparisons • Network – quickly transit around the sub-networks in a complex model and go going directly into a selected subnet • Test – Programmer menu for development work • Help – Sample models, including some in other languages, Help (not yet implemented in 2.1.16 version of SuperDecisions), for now use this old Help file: http://www.superdecisions.com/SuperDecisions_Help.pdf
6. 6. Main Menu Commands• File – New – brings up templates, Open file, Close file, Recent Files, Backups, Import model in .txt format, Export supermatrices to .txt files, Print model report, Old files have .mod extensions, new files have .sdmod extensions• Design – Build a network by creating clusters and nodes and making node connections• Assess/Compare – Perform pairwise comparisons, access the Ratings spreadsheet if there is one• Computations – Synthesize results, look at supermatrices, perform sensitivity, do sanity check for errors and incomplete comparisons• Network – quickly transit around the sub-networks in a complex model and go going directly into a selected subnet• Test – Programmer menu for development work• Help – Sample models, including some in other languages, Help, for now use this old Help file: http://www.superdecisions.com/SuperDecisions_Help.pdf
7. 7. Relative Decision Model• We will demonstrate how to use the SuperDecisions software to create a simple hierarchical relative model for selecting the best of three cars.• In a relative model the alternatives are pairwise compared against the criteria.• In a ratings model the alternatives are rated against standards. See Tutorial 2 for how to build a ratings model.
8. 8. A Three-Level Hierarchy to Choose the Best Car Goal Buy Best Car Price MPG Prestige (Miles per Comfort gallon) Acura TL Toyota Camry Honda Civic
9. 9. 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
10. 10. The Decision Hierarchy as it appears in the SuperDecisions Software Cluster Node All links are among nodes: the cluster link is automatically created because some node(s) in the Criteria cluster are connected to some node(s) in the Alternatives cluster See the SuperDecisions software model: Tutorial_1_Acura_Relative_Model.sdmod
11. 11. Building the Decision Hierarchy• File>New and choose Simple Network(simply leaves you with a blank window) or juststart building on the blank opening screenTo create the Goal Cluster select theDesign command:• Design>Cluster>New brings upthe cluster editing window. Type a name and description for the cluster and set theparameters: font, text size, color,icon (if you want) and save.
12. 12. Decision Hierarchy with a newcluster to hold the Goal Node Double-click on a cluster to minimize it to an icon or expand from an icon.
13. 13. Add Goal Node to Goal Cluster• Design>Node>New to get to the node editing window. Select cluster to add node to, enter goal node name (and description if you wish) selecting parameters as before, and save. For convenience, just use the word Goal again. To display descriptions make sure the Icon on the top menu bar is depressed then hold cursor over node or cluster.
14. 14. Add the Rest of the Clusters and Nodes Double-click a cluster to minimize or expand To re-size a cluster click on bottom right hand button on a cluster and drag. IMPORTANT! The cluster holding the alternatives must be named with some version of the word Alternatives Note: Prefacing Cluster and node names with numbers (prefacing with a allows you to control their order in the supermatrices as number is OK) they are appear in alphabetical order there.
15. 15. Build the Hierarchy in SuperDecisions Step 1. Create the clusters and nodes shown below Or use the Use the Design>Node shortcut to Connexions from menu connect nodes command to connect the Goal Node to the Criteria:To turn on theconnectionshortcut modeleft-click the“connections”icon.
16. 16. Complete the Rest of the Connections Turn on the fan-shaped “Show Connections” icon by clicking it Connect each of the four nodes in the Criteria cluster to all three of the alternative nodes. Hold your cursor over a node – such as “Comfort” -, to display nodes it is connected to outlined in red. When the judgments for these nodes with respect to Comfort have been marked as completed, their window will also appear with a red outline.
17. 17. Connecting Nodes: Menu or Shortcut 1Click the“Make 2connections Left-click the “from” node” icon to Selected nodes are depresseddepress it and outlined in blackand enterthe shortcut 3“make Right-click each “to”connections node (which outlines” mode. them in red) Line then 4 automatically appears from Goal cluster to Criteria clusterTo input a picture for a node or cluster icon use the Design>Node>Edit command , click, the Change Icon command andselect a picture. To add your own pictures to the available collection, copy your picture files into the C:/ProgramFiles/Super Decisions/Icons folder (*.gif files work pretty well).
18. 18. Connect Criteria Nodes to Alternative Nodes SHORTCUT to connect many nodes at once Shift left-click on any “from” node in a cluster - selects all nodes Shift right-click on any “to” node connects all “from” nodes to all “to” nodes Line automatically appears between clusters
19. 19. Remove Unintended Loops A loop will appear on a cluster when a node or node(s) are connected to other node(s) in the same cluster. REMOVING LOOPS Right click on the background of the cluster with the loop and select the Remove self loop command.
20. 20. Unweighted Supermatrix before making any pairwise comparisonsThe nodes connected from a node are shown in the column below thatnode; for example, the Goal node is connected to the criteria nodes andthey are equally weighted at .25 before making pairwise comparisons.Supermatrices are square; every node appears as a column and a row. Thepriorities, that add up to 1.0, are read from the columns. Cluster names Node names Priorities of Criteria nodes
21. 21. Making Pairwise Comparisons• Click on the Goal Node to select it.• Click the pairwise comparison/assessment icon on the menu bar to enter the assessment mode or use the Assess/Compare command.• The Questionnaire Pairwise Comparison Mode opens bydefault. Click on the Matrix tab to switch to the MatrixMode.
22. 22. More About the Compare/Assess Mode There are 5 possible modes for entering assessments; judgments entered in one mode will appear as the equivalent judgment in any other mode.Choose tab indicating whethercomparing nodes or clusters(cluster comparisons not possiblein hierarchies) Selector for parent node of comparisonSelector for cluster containingnodes linked from parent node, tobe compared with respect to itRestore button will bring backoriginal judgments forselected comparison groupwhen revisiting comparisons
23. 23. Example of a Pairwise comparison Matrix in SuperDecisions and in traditional AHP• Only 3 judgments • In the AHP Theoryare necessary view you see 9 judgments Acura Civic Camry Acura 1 8 4 Civic 1/8 1 1/4 Camry 1/4 4 1 Diagonal elements are always 1, so they do not need to be displayed. The elements below the diagonal are always inverses of the AHP reciprocals are shown in judgment in the reciprocal cell above, so they red in SuperDecisions. For do not need to be displayed (e.g. 1/8 8). example, 4.0 means for1/4. aij = 1/ aji
24. 24. Start Making Pairwise Comparisons1. Left-click on Goal node to select it2. Left-click on “make assessments” icon Comparison/Assessment Questionnaire mode appears.3. Switch to the Matrix mode by clicking on matrix tab. Change the comparative phrase 1Prestige is ????times more Preference than 2Price by left-clicking on it and choosing importance.. Note the copy commands. You can then paste into Excel or Word.
25. 25. Enter Judgments (Matrix Mode)1. Enter judgments in cells by typing numbers from Fundamental Scale. The direction of the arrow indicates which criterion is more important. Double-click on arrow to change dominance direction. The first element in the comparative phrase is the dominant one. Up arrows are red, down arrows are blue.2. The current parent node is the Goal node and the Criteria nodes are being compared with respect to it for importance. The inconsistency should be less than 0.10. Inconsistency=0.07685; Derived Priorities Mark completed and move to next comparison
26. 26. Improve Consistency (available only from Matrix Mode)• Click on the Inconsistency button (at top left corner of matrix)• Choose Basic Inconsistency Report; the first cell, Prestige versus MPG, currently has a red 3 in it meaning that MPG are more important than Prestige (see previous view of matrix), but the Best Value of 1.05 (in blue) means Prestige is a little more important than MPG and the inconsistency would be improve down to 0.01 if that were the judgment• Left-click on either the Current or Best Value cell to return to the matrix and input a new value . You can use the suggested value, or a value between it and the original value, or leave it as it is and go to the number 2 most inconsistent judgment (MPG versus Comfort) and change that, and so on. See next slide.
27. 27. Matrix View after ImprovingJudgment of MPG vs Prestige Although the original inconsistency of 0.07 passes the .10 test, it can be improved. New judgment Better Inconsistency of 0.01.
28. 28. Derived Priorities are placed in Supermatrix
29. 29. Other Comparison ModesGraphical Click and drag on circle (NOT the bars) to change judgment Verbal Tracking  – shows which judgment you are on in equivalent matrix view Click button to invert dominance
30. 30. The Questionnaire Mode The Assessment/Compare command opens the pairwise comparison mode by default. Choose the judgment on the left or right side of the zero on the questionnaire line that is nearest to the more important, more preferred, or more likely, node. Here price is more important than prestige. If necessary, and it is here, change the verbal phrase so it reads correctly, as explained below.In the view above the questionnaire opened with the wrong dominance word,“moderately to strongly more Preference”. Left click on the dominance phrase itself to get the menu of possible phrases and select the most appropriate word.
31. 31. Direct Data Assessment Mode Enter direct data in the Direct mode. It may be already normalized, as shown here, or it may be numbers representing costs or distances. Important! Click <Enter> or move away from last judgment entered to make sure it has registeredClick the Invert box when the priorities are inversely related to the data suchas distance, farther is lower priority, or cost, more expensive is lower priority.
32. 32. Weaknesses of using Direct Data • Data may not be as good as judgments in determining your personal priorities. It would usually be better to use your judgment about what the price of a car means to you rather than use the 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 judgments Priorities from data
33. 33. Compare Cars for Prestige and Price Prestige Comparisons Price Comparisons
34. 34. Compare Cars for MPG and Comfort MPG Comparisons and Priorities Comfort Comparisons and Priorities
35. 35. 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 there are no cluster weights and the weighted supermatrix is the same as the unweighted.3. Computations>Limit Supermatrix: The limit matrix is obtained by raising the weighted supermatrix to powers until it converges to give the answer.
36. 36. The Unweighted Supermatrixafter all Judgments Completed
37. 37. Synthesize to get Overall Results• Select Computations>Synthesize or click to get the final results: the priorities of the alternatives. You MUST name the Alternatives cluster with some variation of the word alternatives to get an answer. 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 summing and dividing each by the sum. The Ideals are obtained by dividing the Raw values by the largest Raw value
38. 38. Sanity Check• The Computations>Sanity Check will reveal incomplete comparisons and duplicate goals, among other things. Each time you finish a set of comparisons you must mark it complete before proceeding to the next set. Unintentionally skipped comparisons will also be caught by the Sanity Check.
39. 39. WARNING! No Alternatives FoundThis error message will appear if there is no cluster named someversion of the word alternatives, IN ENGLISH, but for example,3alternatives is an acceptable name. The SuperDecisionssoftware uses this word to find for which nodes it should deliversynthesized priorities extracted from the raw values in the limitsupermatrix. To obtain synthesized priorities for any other nodesgo to the limit supermatrix, get the raw values, and normalizethem yourself. The Normals are the raw values divided by theirsum. The Ideals are the raw values divided by the largest rawvalue.
40. 40. Results obtained from Limit Supermatrix
41. 41. Graphical Sensitivity 1. To do graphical sensitivity select the Computations>Sensitivity command 2. Select Edit>Independent Variable to get to the Sensitivity input selector box and change the Independent Variable to the Goal. The first graph that appears has the first node, alphabetically, selected as the “with respect to” node. It is generally not the one you want. Here you need to select the Goal, not the Acura TL, as the independent variable
42. 42. Graphical Sensitivity (cont’d)Step one. Select theEdit>Independent VariablecommandStep two. In the SelectedNode box highlight thecurrent node (Acura) thenlick Edit.Step three. In the Input Parameter Box select Parameter Type: Supermatrix, the Goal as Wrt Node (“with respect to”) and select one of the criteria as the 1st other node, for example, choose Prestige. Click on the button to the right to get the drop down box with the other choices.
43. 43. Getting Sensitivity Graph for Prestige Show Selected Node Box Set Parameters Box1 2 Sensitivity Graph for Selected node(s)Updated Parameters – click Update for results Priority of Prestige is given on x-axis; vertical line starts at Prestige priority 3 4 of 50%; car priorities for Prestige=50% priority are shown by intersections with vertical line.
44. 44. Interpreting Sensitivity of PrestigeAt Prestige = 50%, Acura is best At Prestige = 9.2% (actual priority in model), Civic is bestClick and drag vertical line to change priority of Prestige on horizontal axis from 0.5 to 0.1.The analysis: If your priority is less than about 25% for Prestige, the Honda is the carto buy. For any priority greater than that, the Acura is your best car.
45. 45. Priorities of all Nodes in Model • Select Computations>Priorities command to see the priorities of all nodes in model • “Limiting priority” column shows priority of Prestige compared to all the other nodes in the entire model. • “Normalized by Cluster” column shows the priority of Prestige (.096) compared to the other criteria in its cluster. • Drag the vertical line from .5 to . 096 on the x-axis in Sensitivity to show the priorities of the cars at the model priority of .096 for Prestige.
46. 46. Dynamic SensitivitySelect Computations>New Sensitivity to get into Dynamic Sensitivity Mode Click on “Node for Sensitivity” selector button at right and change from Goal Node, shown here, to 1Prestige.
47. 47. Dynamic Sensitivity - Prestige The Prestige parameter can be dragged from 0.00 to 1.00. At 0.50, the priorities of the cars are the same as the overall synthesized result priorities of 0.344, 0.200 and 0.456.
48. 48. Dynamic Sensitivity At a parameter value of 1.00 for Prestige the most prestigious car, the Acura is clearly the best choice.
49. 49. Putting Subcriteria into a Hierarchical Model • Create separate clusters for the subcriteria of the criteria that will have subcriteria. • Price has subcriteria of initial cost and maintenance, which then connect to the cars. • Comfort has subcriteria of Ride and Driving Performance which then connect to the cars. • Prestige and MPG have no subcriteria and connect directly to the cars.
50. 50. Getting BackupsThe most recent backup is at the top of the list. Double-click on the name of the version you wantto open it in a new window with a complete history of backups to its time included. Backups aremade at frequent intervals. However, it is still a good idea to do versioning occasionally yourself,saving the file with a different version name: Vacation Rev 1.sdmod, Vacation Rev 2.sdmod, andso on.
51. 51. Exporting SupermatricesThe following files may be exported as .txt files using the File>Export command: Unweighted Supermatrix Weighted Supermatrix Limit Supermatrix Cluster MatrixImport into Excel using the File>Open command . Be sure to select All Files for type of file with the Open command so the .txt file you exported will appear. Click yes through the wizard to open in Excel.
52. 52. Reports• The Computations>Full Report command and the File>Print command both generate the same HTML file of reports about the model. You may use the Print Preview version, or save as a .html file. It gives the names and descriptions of the nodes and clusters and important priorities.