Title: Issues in decision support under preferential uncertainty Decision making based on simple interval MAVT modelling with the WINPRE software
1Issues in decision support under preferential
uncertaintyDecision making based on simple
interval MAVT modelling with the WINPRE software
- Jyri Mustajoki
- Raimo P. Hämäläinen
- Systems Analysis Laboratory
- Helsinki University of Technology
- www.sal.hut.fi
2Outline of the presentation
- Multiattribute value tree analysis
- Decision analytical approach to model the
decision makers preferences - Can be applied e.g. in e-Democracy to get a view
of different stakeholders preferences - Intervals to describe uncertainty
- An easy-to-use method Interval SMART/SWING
- Practical and procedural issues related to the
use of Interval SMART/SWING
3Multiattribute value tree analysis
- Value tree
- Overall value of alternative x
-
- n number of attributes
- wi weight of attribute i
- xi consequence of alternative x with respect
to attribute i - vi(xi) rating of xi
4Ratio methods in weight elicitation
- SWING
- 100 points to the most important attribute change
from its lowest to its highest level - Fewer points to other attribute changes
reflecting their relative importance - Weights by normalizing the sum to one
- SMART
- 10 points to the least important attribute
- Otherwise similar
5Intervals to describe uncertainty
- Uncertain replies modeled as intervals instead of
pointwise estimates - Intervals can describe e.g.
- Preferential uncertainty
- Incomplete information
- Uncertainty about the consequences of the
alternatives - As a result, overall value intervals of the
alternatives - Analyzed with dominance concepts
6Classification of ratio methods
Exact point estimates Interval estimates
Minimum number of pairwise judgments SMART, SWING Interval SMART/SWING
More than minimum number of judgments allowed AHP, Regression analysis PAIRS, Preference programming
7 Interval SMART/SWING
- The reference attribute given any (exact) number
of points - Points to the other attributes given as intervals
8Feasible region of the weights, S
- Bounded by max / min ratios of the given points
- ref points given to the reference
attribute - mini / maxi minimum / maximum points given
to attribute i - Normalization ?wi1
9Overall value intervals
- One can similarly give intervals to the ratings
of the attributes - As a result, overall value intervals
for the alternatives - Describe the possible
variation of the overall values
10Pairwise dominance
- A dominates B pairwisely, if the value of A is
greater than the value of B for every feasible
weight combination, i.e. if - S feasible region of weights
- vi(xi) lower bound of vi(xi)
- vi(yi) upper bound of the rating of vi(yi)
- Solved by linear programming
11WINPRE software
- Weighting methods
- Preference programming (interval AHP)
- PAIRS
- Interval SMART/SWING
- Interactive graphical user interface
- E.g. dominance relations identified on-line when
making changes to intervals - Available free for academic use
- www.decisionarium.hut.fi
12Vincent Sahid's job selection example
- (Hammond, Keeney and Raiffa, 1999)
13Consequences table
Job A Job B Job C Job D Job E
Monthly salary 2000 2400 1800 1900 2200
Flexibility of work schedule Moderate Low High Moderate None
Business skills development Computer Manage people, computer Operations, computer Organization Time mana-gement, multiple tasking
Vacation (annual days) 14 12 10 15 12
Benefits Health, dental, retirement Health, dental Health Health, retirement Health, dental
Enjoyment Great Good Good Great Boring
14Imprecise rating of the alternatives
15Interval SMART/SWING weighting
16Value intervals and dominances
- Jobs C and E
dominated - ? Can be eliminated
- One can continue the process by narrowing the
weight ratio intervals - Easier as Jobs C and E already eliminated
17Our research topics
- What are the benefits of the interval SMART/SWING
approach? - Role of the reference attribute
- What if other than worst/best SMART/SWING?
- Use of interval SMART/SWING in group decision
making
18Benefits of interval SMART/SWING
- SMART and SWING are simple and relatively well
known methods - Intervals provide an easy way to model
uncertainty - Interval SMART/SWING preserves the cognitive
simplicity of the original methods - ? Behaviorally Interval SMART/SWING is likely to
be easily adapted
19Comparison with PAIRS
- In PAIRS, constraints given for all the possible
ratios of the weights - The number of constraints
- Interval SMART/SWING 2 (n -1)
- PAIRS n (n - 1)
- ? In PAIRS, the needed workload can become high
compared to its advantages - In our simulation study, the additional
constraints of PAIRS did not produce relatively
many new dominances
20Choice of the reference attribute
- All the constraints on the weight ratios between
the reference attribute and some other attribute - ? Feasible region depends on the choice of the
reference attribute - Aim to make the process procedurally efficient
- ? The reference attribute should be selected so
that as many alternatives as possible become
dominated
21Example
- Attr. 1 given 100 points
- Attr. 2 given 50-200 points
- Attr. 3 given 100-300 points
- ? Weight ratios
- ½ w1 ? w2 ? 2 w1
- w1 ? w3 ? 3 w1
- No explicit information about the weight ratio
between attributes 2 and 3 given
22Different attributes as a reference
- Attr. 1 as a reference
- Attr. 2 50 100 points
- Attr. 3 100 300 points
- Attr. 1 50 100 points
- Attr. 2 as a reference
- Attr. 3 67 400 points
- Attr. 1 33 100 points
- Attr. 2 25 150 points
- Attr. 3 as a reference
23Simulation study
- Comparison of strategies with different
attributes as a reference - The most important one
- The least important one
- Intermediate ones
- Same relative imprecision assumed on each
strategy - Weight ratios and ratings obtained from normal
distributions on consequences
24How to select the reference attribute?
- In the simulation, most dominance relations
obtained with the strategy having the most
important attribute as a reference - Good initial choice for a reference attribute
- Surely meaningful to the DM
- Differences between the strategies small
- If the DM can easily identify an attribute
containing least imprecision, this should be
selected as a reference attribute instead of the
most important one.
25Interval methods in group decision support
- Interval model applied to include the range of
preferences of all the different DMs - E.g. the feasible region of the weights consists
all the feasible weight ratios of all the DMs - ? Any dominated alternative is dominated for all
the individuals - The individual DMs can use either point estimates
or intervals in their preference elicitation
26Interval methods in group decision support
- If the range of the DMs preferences is wide
- ? Feasible region becomes wide
- ? Not likely to obtain dominance relations
between the alternatives - The process can continue by collaboratively
trying to tighten the intervals - E.g. through negotiation
- May not be easy
27Conclusions
- Interval SMART/SWING
- An easy method to model uncertainty by intervals
- Intervals can also be used to describe the range
of preferences within the group - How do the DMs use the intervals?
- Procedural and behavioral aspects should be
addressed - Linear programming algorithms involved
- Computational support needed
- WINPRE software available for free
28References
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