Issues in decision support under preferential uncertainty Decision making based on simple interval MAVT modelling with the WINPRE software

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Issues 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

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Outline 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

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Multiattribute 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

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Ratio 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

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Intervals 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

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Classification 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
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Interval SMART/SWING

• The reference attribute given any (exact) number
  of points
• Points to the other attributes given as intervals

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Feasible 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

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Overall 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

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Pairwise 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

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WINPRE 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

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Vincent Sahid's job selection example

• (Hammond, Keeney and Raiffa, 1999)

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Consequences 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
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Imprecise rating of the alternatives
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Interval SMART/SWING weighting
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Value 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

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Our 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

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Benefits 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

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Comparison 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

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Choice 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

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Example

• 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

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Different 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

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Simulation 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

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How 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.

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Interval 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

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Interval 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

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Conclusions

• 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

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