Logical Decisions - Classweb

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always a complete set of utilities available. If you don't want to enter all the ratios required by the AHP process (and sometimes quite a lot of ratios are required), you can stop any time the computed utilities seem reasonable. Estimates of Consistency in AHP The AHP process asks you to enter more performance ratios than are strictly necessary to compute a set of utilities for the alternatives. Because of this, your performance ratios are likely to be inconsistent. To provide guidance on how consistent you are, the developers of the AHP method suggest using a statistic called the "consistency ratio (CR)." The CI compares your matrix to a random matrix of the same size. The higher the CR, the more inconsistent you are. The developers of AHP suggest that if the CR for your matrix is greater than 0.1 you should adjust your ratios to make them more consistent. Two intermediate statistics are used to compute the CR. The first, called "ë max" is the principal eigenvalue of your AHP matrix. ë max is the matrix product of your AHP matrix and the vector of the (unadjusted) utilities for the alternatives. (Don't worry if this is unclear. You won't be tested on it.) The second intermediate statistic is called the "consistency index (CI)." The CI is an absolute measure of consistency. Its computed from ë max as CI = (ë max - n)/(n - 1), where n is the number of alternatives. The consistency ratio CR is computed by dividing the CI for your matrix by the CI for a "random" matrix of the same size. The discussion on page 7-15 tells you how to assess common units with the Analytic Hierarchy Process in LDW. Computing Common Units With AHP SUFs LDW lets you combine the AHP and SUF methods for computing common units in a method called AHP SUFs. In this method, you will still define a scale and range for your measure and levels for your alternatives on the measure. However, instead of using the normal SUF assessment process, you will use an AHP matrix to define a SUF for the measure. 9-30 Section 9 -- In Depth
You begin the process by selecting a subset of your alternatives to use in the AHP matrix. These alternatives must have levels within the range for the measure defined in its measure dialog box. After you select your alternatives, you continue with the AHP assessment process as described above. When you are done, each alternative will have an associated utility as computed from the AHP matrix. Since the alternatives also have levels, we can compare the levels and utilities and use them to define a SUF. This is done in one of two ways depending on the alternatives you selected. If you selected alternatives that cover only part of the measure's range, LDW uses the unadjusted AHP utilities to define the utility for each alternative's level. LDW assigns the measure's least preferred level a utility of zero and its most preferred level a utility of one. These endpoints are connected to the utilities computed using AHP matrix with straight lines. If you selected alternatives that cover the measure's entire range, a slightly different process is used. The AHP utilities are first adjusted to range from zero to one (as in the Adjusted AHP Measure Levels method) and are then associated with the measure levels. The utilities are then connected with straight lines to form a complete SUF. Establishing the Importance of Each Measure After you have made the measures comparable by converting them to common units, the next step is to define how to combine the utilities for individual measures into utilities for the goals. LDW also quantifies an alternative's performance on a goal in units of utility. A goal's utility is computed using a function that combines the utilities of a goal's active members into a utility for the goal. The formula used to combine the utilities is a Multiple-measure Utility Function or MUF (pronounced "muff"). Higher level goals can have a MUF that combines utilities for not only measures but also utilities for lower level goals computed using their own MUFs. Section 9 -- In Depth 9-31
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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
Page 225 and 226: Figure 8-50. Dialog box for Prefere
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Page 229 and 230: copies the selected objects to the
Page 231 and 232: analysis with the skeleton analysis
Page 233 and 234: Figure 8-55. Dialog box for File::I
Page 235 and 236: the other measures. The measure nam
Page 237 and 238: The idea of the Import Structure op
Page 239 and 240: Next, LDW asks you if it should app
Page 241 and 242: Other Options utility function for
Page 243: In addition, the Window menu contai
Page 247 and 248: In Depth Introduction This section
Page 249 and 250: A third example is a portfolio deci
Page 251 and 252: Each alternative has a raw score (c
Page 253 and 254: into more specific goals continues
Page 255 and 256: Measures in LDW You define measures
Page 257 and 258: computed measure levels to common u
Page 259 and 260: Converting the Measures to Common U
Page 261 and 262: Figure 9-2. Example of linear (stra
Page 263 and 264: For an example of the mid-level spl
Page 265 and 266: Since U(L0) = U(80) = 0 and U(L1) =
Page 267 and 268: Figure 9-5. Summary of SUF assessme
Page 269 and 270: describe two alternatives: A, which
Page 271 and 272: with equal chances of 40 and 70 per
Page 273 and 274: In the original formulation of the
Page 275: 1 Equal Importance Two activities c
Page 279 and 280: Figure 9-7. Effects of goals with a
Page 281 and 282: 0.5. Then the weight assigned to "P
Page 283 and 284: ! You can use the "Smarter Method"
Page 285 and 286: allocates this weight before comput
Page 287 and 288: nth root of the product of the rati
Page 289 and 290: Figure 9-8. Summary of estimating t
Page 291 and 292: on the decision maker's response, L
Page 293 and 294: Figure 9-10. MUF assessment figure
Page 295 and 296: Now think of adjusting P so that th
Page 297 and 298: Another approach is to use the rang
Page 299 and 300: Figure 9-12. Quantitative range vs.
Page 301 and 302: If a measure’s range changes, LDW
Page 303 and 304: Figure 9-14 is an example of the ov
Page 305 and 306: Similarly, a single member can have
Page 307 and 308: chance having 160 hp (the most pref
Page 309 and 310: A probability of less than 0.5 for
Page 311 and 312: Interpreting the Ranking Results LD
Page 313: S E C T I O N Examples 10
Page 316 and 317: the idea that other manufactures an
Page 318 and 319: The completed goals hierarchy is sh
Page 320 and 321: Buying a House The ranking results
Page 322 and 323: Figure 10-5. Goals hierarchy for bu
Page 324 and 325: Overall goal Quality goal Costs goa
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The preference assessments were don
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Figure 10-9. Goals hierarchy for re
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! Noise, ! Agricultural Impacts, an
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S E C T I O N Commands Summary 11
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Assess Menu Edit Menu The Assess me
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File Menu Edit::Insert Lets you add
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utility function” if the active g
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Matrix Menu ! Hierarchy -- options
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Results::Dynamic Sensitivity See th
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Review::Compute Utilities Compute t
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Tradeoff Menu View Menu LDW display
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S E C T I O N Glossary 12
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Common Units Certainty Equivalent C
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LDW File Level Lottery Measure assi
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MUF MUF Formula See also: Alternati
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Preference Set Probabilistic Level
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Tradeoff Trial program decides whic
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Bibliography B
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The classic reference on multiple m
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Appendix This appendix describes th
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= .125 Thus the weight for cost is
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Index adjusted AHP ................
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computing ................8 - 3 int
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