Logical Decisions - Classweb

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MUF MUF Formula See also: Alternative Uncertainty Graph option, Level, Measure, MUF, Probabilistic Level, Sample, Simulation Options option, SUF, Trial, Uncertainty Summary option, Utility. A Multi-measure Utility Function (MUF) is the formula that combines the utilities for the individual measures computed by the SUFs into the utility for a goal. A MUF consists of two parts: a SUF for each measure and a set of scaling constants (called small ks) that determine the relative importance of the measures. (For goals with other goals as members, MUFs for the member goals may replace SUFs. The scaling constants are similar in both cases.) LDW uses two types of MUF Formulas to combine the measures -- an additive form where the small ks can be interpreted as weights and a multiplicative formula that includes an additional scaling constant called big K. Big K can be interpreted as the degree of interaction between the measures. See also: Alternative, Big K, Define Interactions option, Measure, MUF Formula, Small k, SUF, Tradeoff, Utility, Weight. LDW uses two formulas for MUFs. The additive formula is: U g(X) = k1U 1(X) + k2U 2(X) + ... + knU n(X), where U g(X)= is the utility of alternative X for the goal g, U i(X)= the utility of alternative X for the ith member of g, and k = the scaling constant small k for the ith member of g. i The additive formula requires that the small ks sum to 1.0 and that big K = 0.0. The additive formula is used as the default formula, when the Additive MUF option is selected and when big K is computed to equal 0.0. The second MUF formula is the multiplicative formula: U g(X) = ((1 + Kk1U 1(X))(1 + Kk2U 2(X))...(1 + KknU n(X)) - 1)/K, where g U (X) = the utility of alternative X for goal g, K= the scaling constant big K for g, 12-6 Section 12 -- Glossary
Nominal Utility Point Estimate k i= the scaling constant small k for member i of g, and U (X)= the utility of alternative X for member i i The multiplicative MUF formula is used when a non-additive option is selected in Define Interactions. The formula has three interesting limits -- If big K equals 0.0, the formula reduces to the additive formula. If big K equals -1.0, the formula reduces to U g(X) = (1 - U 1(X))(1 - U 2(X))...(1 - U n(X)) + 1, which equals 1.0 if U i(X) = 1.0 for any i. As big K gets very large, the formula becomes U g(X) = U 1(X)U 2(X)...U n(X), which equals 0.0 if U i(X) equals 0.0 for any i. Intermediate values of big K have intermediate degrees of interaction. Big Ks less than 0.0 mean that a high utility on an individual member can result in a high overall utility (constructive interaction), while big K greater than 0.0 indicates that a low utility on an individual member can result in a low overall utility (destructive interaction). See also: Additive MUF, Alternative, Big K, Define Interactions, Goal, Member, MUF, Small k, Utility. A nominal utility is assigned to all members of a goal when the utility is not directly specified. The nominal utility is assigned when the goal is defined and is generally set to 1.0, so that all members of the goal are assumed to have their most preferred levels if their level is not directly specified. This situation occurs while assessing tradeoffs, when a single measure is used to represent a goal in a tradeoff. When the tradeoff questions are displayed, the decision maker is asked to assume that the representative measure has a certain utility and that all other members of the goal have the nominal utility. See also: Goal, Measure, Member, Tradeoff, Utility. A point estimate for a measure level is a single number that will be the measure's level with certainty. This is in contrast to a probabilistic level, where a measure's level is not known with certainty and must be described with a probability distribution. See also: Level, Measure, Probabilistic Level. Section 12 -- Glossary 12-7
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Logical Decisions Decision Support
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Table of Contents Table of Contents
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Assessing Weights with Weight Ratio
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Assessing Interactions Between Meas
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Introduction Real decisions aren't
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S E C T I O N Requirements and Inst
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"Logical Decisions". This program g
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Quick Start Introduction This secti
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Defining goals and measures. In LDW
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Figure 3-1. The SUF for "Years of E
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weights of the measures. All of the
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S E C T I O N Basic Tutorial 4
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Figure 4-1. Tutorial overview. 4-2
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Now lets make sure the alternatives
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Assume you have decided that you wi
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Next we will enter the measures for
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Defining Preferences The alternativ
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1. Select the Assess::Common Units
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almost equally unacceptable, while
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1. Select the Assess::Common Units
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When you do this, the tradeoff grap
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1. Select "Performance" and "Price"
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8. Click on the "Equal" button to t
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Figure 4-11. Display generated by R
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Figure 4-13. Overall ranking for tr
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Figure 4-15. Graph showing sensitiv
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You can see the completed introduct
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Advanced Tutorial This tutorial sec
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Probabilities There is a problem wi
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This information indicates that the
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A uniform distribution is defined b
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On the left is a list of the possib
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Figure 5-2. Example of Results::Unc
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screen a large database for the alt
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9. LDW will ask if you want to appe
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commit to buying their truck before
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see that the rankings for all the a
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S E C T I O N Using LDW 1: Structur
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The Edit::Insert option. The Insert
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! Summary -- view a dialog box that
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structure like an organization char
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If you check the Show Assessment St
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saves it for later pasting. When yo
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You can create a new Matrix view by
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The quick entry view shows the alte
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Structuring Goals The goals in an L
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these two fields to describe each m
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the hierarchy. In the Matrix view,
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! Point Estimate -- use a single nu
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Figure 6-12. Example of a measure l
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Figure 6-14. Example of a measure l
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pass, LDW replaces each probabilist
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Figure 6-17. Dialog box for definin
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Figure 6-18. Measure Category Dialo
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S E C T I O N Using LDW 2: Assessin
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measure utility functions for the g
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information as possible when you ch
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measures with categories require mu
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The "Reset" button deletes any asse
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You can change the shape of the cur
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Figure 7-4. Utility Assessment Scre
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very different from the average of
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Figure 7-6. Assessment matrix for A
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You can, however, leave the assessm
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properties dialog box can be select
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the same level. LDW provides a grap
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options in the Hierarchy menu to ad
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The check box labeled "Allow Repres
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Next you will see a tradeoff assess
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The Tradeoff::Use Alternatives to S
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Figure 7-13. Example of Direct Entr
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You can think of the importance num
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Figure 7-15. Assessment Screen for
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When you have selected two members
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("importance strength") that best d
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clicking on the "Initialize" button
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Set a Small k. The Enter Small k op
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select the tradeoff you would like
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Figure 7-18. Effects of consistency
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Using LDW 3: Reviewing Results Intr
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The curve shows how the utility fun
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The tradeoff graph has one measure
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When you select the option, you are
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the relative weights of the "Price"
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epresents a computer alternative wi
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Figure 8-11. Example of Review::Ass
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e true even if the measure has a ve
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an analysis are included in exactly
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Graph Weights The Graph Weights dis
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Figure 8-16. Results::Rank Alternat
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Figure 8-18. Dialog box for Results
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You can use the measure equivalents
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simulation for each alternative usi
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Sensitivity Graphs Sensitivity grap
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You can view a sensitivity table by
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Figure 8-28. Example of Results::Sc
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Figure 8-30. Example of Results::Sc
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In the dialog box, you are asked to
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Figure 8-34. Dialog box for Results
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Graph an Alternative The graph an a
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Figure 8-38. Example of Results::Gr
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Finally, the two radio buttons on t
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Figure 8-43. Example of Results::Co
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Printing and Saving Windows You can
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The dialog box will show you the fi
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Figure 8-45. Dialog box for Edit::C
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Changing the range for utility. You
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Figure 8-50. Dialog box for Prefere
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the current color for that type of
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copies the selected objects to the
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analysis with the skeleton analysis
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Figure 8-55. Dialog box for File::I
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the other measures. The measure nam
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The idea of the Import Structure op
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Next, LDW asks you if it should app
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Other Options utility function for
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In addition, the Window menu contai
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In Depth Introduction This section
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A third example is a portfolio deci
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Each alternative has a raw score (c
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into more specific goals continues
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Measures in LDW You define measures
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computed measure levels to common u
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Converting the Measures to Common U
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Figure 9-2. Example of linear (stra
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For an example of the mid-level spl
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Since U(L0) = U(80) = 0 and U(L1) =
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Figure 9-5. Summary of SUF assessme
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describe two alternatives: A, which
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with equal chances of 40 and 70 per
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In the original formulation of the
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1 Equal Importance Two activities c
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You begin the process by selecting
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Figure 9-7. Effects of goals with a
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0.5. Then the weight assigned to "P
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! You can use the "Smarter Method"
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allocates this weight before comput
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nth root of the product of the rati
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Figure 9-8. Summary of estimating t
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on the decision maker's response, L
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Figure 9-10. MUF assessment figure
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Now think of adjusting P so that th
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Another approach is to use the rang
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Figure 9-12. Quantitative range vs.
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If a measure’s range changes, LDW
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Figure 9-14 is an example of the ov
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Similarly, a single member can have
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Page 311 and 312: Interpreting the Ranking Results LD
Page 313: S E C T I O N Examples 10
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Page 333: S E C T I O N Commands Summary 11
Page 336 and 337: Assess Menu Edit Menu The Assess me
Page 338 and 339: File Menu Edit::Insert Lets you add
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Page 342 and 343: Matrix Menu ! Hierarchy -- options
Page 344 and 345: Results::Dynamic Sensitivity See th
Page 346 and 347: Review::Compute Utilities Compute t
Page 348 and 349: Tradeoff Menu View Menu LDW display
Page 351: S E C T I O N Glossary 12
Page 354 and 355: Common Units Certainty Equivalent C
Page 356 and 357: LDW File Level Lottery Measure assi
Page 360 and 361: Preference Set Probabilistic Level
Page 362 and 363: Tradeoff Trial program decides whic
Page 365: Bibliography B
Page 368 and 369: The classic reference on multiple m
Page 371 and 372: Appendix This appendix describes th
Page 373: = .125 Thus the weight for cost is
Page 377 and 378: Index adjusted AHP ................
Page 379: computing ................8 - 3 int
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