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Decision analysis by interval SMART/SWING. Jyri Mustajoki Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi. Multiattribute Value Tree Analysis. Value tree: Value of an alternative x (additive): w i is the weight of attribute i

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decision analysis by interval smart swing

Decision analysis by interval SMART/SWING

Jyri Mustajoki

Raimo P. Hämäläinen

Systems Analysis Laboratory

Helsinki University of Technology

www.sal.hut.fi

multiattribute value tree analysis
Multiattribute Value Tree Analysis
  • Value tree:
  • Value of an alternative x (additive):

wi is the weight of attribute i

vi(xi) is the component value of an alternative x in respect of an attribute i

ratio methods in weight elicitation
Ratio methods in weight elicitation

Questions of interest - new alternative ways:

  • Reference attribute (Are there other than worst/best = SMART/SWING?)
  • Relationship to direct weighting?
  • Uncertain replies modelled as intervals
  • Uncertain reference considered as an interval
  • Behavioral and procedural benefits and problems
attribute weighting
Attribute weighting

SWING

  • 100 points to the most important attribute change from its lowest level to the highest level
  • Fewer points to other attributes denoting their relative importance
  • Weights elicited by normalizing the sum of the points to one

SMART

  • 10 points to the least important attribute
interval decision analysis methods
Interval decision analysis methods
  • Intervals used to describe impreciseness
  • Preference Programming (Interval AHP)
    • Arbel, 1989; Salo and Hämäläinen 1995
  • PAIRS (Preference assessment by imprecise ratio statements)
    • Salo and Hämäläinen, 1992
  • PRIME (Preference ratios in multiattribute evaluation)
    • Salo and Hämäläinen, 1999
generalizing smart and swing
Generalizing SMART and SWING
  • Relaxing the reference attribute to be any attribute
  • Allowing the DM to reply with intervals instead of exact point estimates
  • Allowing also the reference attribute to be an interval
simplified pairs
Simplified PAIRS
  • PAIRS
    • Constraints on any weight ratios

 Feasible region S

  • Generalized ratio methods simplified cases of PAIRS
relaxing the reference attribute to be any attribute
Relaxing the reference attribute to be any attribute
  • Generalization of SMART/SWING or direct weighting
  • Weight ratios calculated as ratios of the given points

 Technically no difference to SMART and SWING

  • Possibility of behavioral biases
    • Proper guidance to the DMs
    • More research needed
interval smart swing
Interval SMART/SWING
  • The reference attribute given any (exact) number of points
  • Points to non-reference attributes given as intervals
interval smart swing1
Interval SMART/SWING
  • Max/min ratios of points constraint the feasible region of weights
    • Values calculated with PAIRS
  • Pairwise dominance
    • A dominates B pairwisely, if the value of A is greater than the value of B for every feasible weight combination
an example
An example
  • Three attributes: A, B, C
  • Preferences of the DM:
  • Two cases considered:

1. A chosen as reference attribute (100 points)

 Other attributes (B, C) given 50-200 points

2. B chosen as reference attribute (100 points)

 A given 50-200 points, C given 100 points

reference attribute
Reference attribute
  • A as a reference attribute
feasible region
Feasible region
  • A as a reference attribute
reference attribute1
Reference attribute
  • B as a reference attribute
feasible region1
Feasible region
  • B as a reference attribute
choice of the reference attribute
Choice of the reference attribute
  • Only the weight ratio constraints including the reference attribute are given

 Feasible region depends on the choice of the reference attribute

  • Choice of the reference attribute?
    • Attribute with least uncertainty
    • Easily measurable attribute, e.g. money
using an interval on the reference attribute
Using an interval on the reference attribute
  • Meaning of the intervals
    • Ambiguity
  • Constraints for the weight ratios:
  • Every constraint is bounding the feasible region
using an interval on the reference attribute3
Using an interval on the reference attribute
  • Are the DMs able to compare the intevals?
  • The final step of generalizations is to relax the weight ratio constraints to be any constraints

 PAIRS method

winpre software
WINPRE software
  • Weighting methods
    • Preference programming
    • PAIRS
    • Interval SMART/SWING
an example1
An example
  • Vincent Sahid's job selection (Hammond, Keeney and Raiffa, 1999)
the results1
The results
  • Jobs C and E dominated

 Eliminated from subsequent analyses

  • Process could be continued by defining the attributes more accurately
    • Easier as fewer alternative
conclusions
Conclusions
  • Interval SMART/SWING
    • An easy method to model uncertainty by intervals
  • Linear programming algorithms involved
    • Software needed
    • WINPRE introduced
  • Does the DMs understand the intervals?
    • More research needed
references
References

Arbel, A., 1989. Approximate articulation of preference and priority derivation, European Journal of Operational Research 43, 317-326.

Hammond, J.S., Keeney, R.L., Raiffa, H., 1999. Smart Choices. A Practical Guide to Making Better Decisions, Harvard Business School Press, Boston, MA.

Salo, A., Hämäläinen, R.P., 1992. Preference assessment by imprecise ratio statements, Operations Research 40 (6) 1053-1061.

Salo, A., Hämäläinen, R.P., 1995. Preference programming through approximate ratio comparisons, European Journal of Operational Research 82, 458-475.

Salo, A., Hämäläinen, R.P., 1999. PRIME - Preference ratios in multiattribute evaluation. Manuscript. Downloadable at http://www.sal.hut.fi/ Publications/pdf-files/Prime.pdf