Logical Decisions - Classweb
Logical Decisions - Classweb Logical Decisions - Classweb
Different preference assessment methods have different traditions for deciding which goals should have a MUF. The Smart and Smarter methods often use a single overall MUF. The AHP approach generally has a MUF for each goal. The tradeoff and pairwise weight ratio methods can use either approach. Interactions apply to all the members of a MUF. If you want to have only a few particular members interact, you must include them in their own MUF. You should include members that interact under their own goal and make sure that that goal has its own MUF. In the discussions below we will call the members of a goal's MUF the "active members" for the goal. Representatives for Goals With a MUF. LDW will include goals that have their own MUF in the MUF for a higher level goal. Often it is difficult to answer preference assessment questions involving a goal because it is hard to interpret the meaning of different levels of utility for a goal. It may also be hard to remember the measures and sub-goals that are its active members and their importances. Therefore LDW allows you to select a representative for the goal in several weight assessment methods. The representative can be any measure below the goal in the goals hierarchy. It can also be any sub-goal with its own MUF below the goal in the goals hierarchy. The representative replaces the goal in the preference assessment questions for the MUF the goal is a member of. LDW computes the goal's weight based on the representative's weight in the MUF for the goal and the representative's weight in the MUF the goal is a member of. Here is a simple example. In the tutorial example, a "Performance" goal includes "Power" and "Fuel Economy" measures. The "Performance" goal and a "Price" measure make up the "Overall" goal (we'll assume that the "Styling" measure has been deleted). Suppose "Power" and "Fuel Economy" are assessed equal weights of 0.5 in the "Performance" goal's MUF. Now suppose that "Power" is selected as the representative for the "Performance" goal in the "Overall" goal's preference assessment. Suppose the "Power" and "Price" measures are also assessed equal weights of 9-34 Section 9 -- In Depth
0.5. Then the weight assigned to "Performance" will be 0.5 divided by the weight for "Power" in its MUF, which is also 0.5. This means that in the "Overall" goal's MUF, "Price" will have a weight of 0.5 and "Performance" will have a weight of 1.0. After LDW has adjusted these weights to sum to one, "Price" will have a weight of 0.33 and "Performance" will have a weight of 0.67. Note that LDW does not include the representative in the MUF instead of the goal it represents. The representative is just a tool that helps you define the weight that LDW should assign to the goal in the MUF it is a member of. For LDW to compute a goal's utility when only its representative's level has been defined, it must make an assumption about the utilities of the goal's other members. Therefore, when you define a goal LDW asks you to specify a nominal utility. LDW temporarily assigns this nominal utility to all of the goal's members, except its representative, when doing tradeoffs. This allows LDW to estimate the goal's utility as follows: U g(X r = x) = krU r(x) + k1U nom + ... + knUnom where = krU r(x) + (1 - k r)Unom U g(X r = x) = goal g's utility when its representative r has level x and the other members have the nominal utility, k r = the small k for the representative measure, U r(x) = the utility of level x for the representative measure, U nom = the nominal utility assigned to other members of the goal. LDW applies this formula recursively if the goal's representative is a member of a goal below it in the hierarchy. The formula is Section 9 -- In Depth 9-35
- 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 and 276: 1 Equal Importance Two activities c
- Page 277 and 278: You begin the process by selecting
- Page 279: Figure 9-7. Effects of goals with a
- 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
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- Page 309 and 310: A probability of less than 0.5 for
- Page 311 and 312: Interpreting the Ranking Results LD
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- 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
- Page 326 and 327: The preference assessments were don
- Page 328 and 329: Figure 10-9. Goals hierarchy for re
0.5. Then the weight assigned to "Performance" will be 0.5<br />
divided by the weight for "Power" in its MUF, which is also 0.5.<br />
This means that in the "Overall" goal's MUF, "Price" will have a<br />
weight of 0.5 and "Performance" will have a weight of 1.0. After<br />
LDW has adjusted these weights to sum to one, "Price" will have a<br />
weight of 0.33 and "Performance" will have a weight of 0.67.<br />
Note that LDW does not include the representative in the MUF<br />
instead of the goal it represents. The representative is just a tool<br />
that helps you define the weight that LDW should assign to the<br />
goal in the MUF it is a member of.<br />
For LDW to compute a goal's utility when only its representative's<br />
level has been defined, it must make an assumption about the<br />
utilities of the goal's other members. Therefore, when you define<br />
a goal LDW asks you to specify a nominal utility. LDW<br />
temporarily assigns this nominal utility to all of the goal's<br />
members, except its representative, when doing tradeoffs.<br />
This allows LDW to estimate the goal's utility as follows:<br />
U g(X r = x) = krU r(x) + k1U nom + ... + knUnom where<br />
= krU r(x) + (1 - k r)Unom U g(X r = x) = goal g's utility when its<br />
representative r has level x and the<br />
other members have the nominal<br />
utility,<br />
k r<br />
= the small k for the representative<br />
measure,<br />
U r(x)<br />
= the utility of level x for the<br />
representative measure,<br />
U nom<br />
= the nominal utility assigned to<br />
other members of the goal.<br />
LDW applies this formula recursively if the goal's representative<br />
is a member of a goal below it in the hierarchy. The formula is<br />
Section 9 -- In Depth 9-35
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