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S ystemsAnalysis LaboratoryHelsinki University of Technology

WINPRE - Workbench for Interactive Preference Programming

Raimo P. Hämäläinen

Jyri Helenius

http://www.hut.fi/Units/Systems.Analysis

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Interval MCDA methods:

• PAIRS = Preference Assessment by Incomplete Ratio Statements (Salo ,Hämäläinen OR 1992)

• SPAIRS = Simple PAIRS = Interval SMART/SWING (New method)

• Interval AHP-Preference programming (Salo,Hämäläinen MCDM 1991,EJOR 1995)

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Related Work• Non-hierarchical models:

– UTA (Jacquet-Lagreze & Siskos 1982): • Additive utility function estimated from regression

analysis of ordinal preference statements

– HOPIE (Weber 1985):• Constraints on additive or multiplicative utility

function from value intervals and holistic judgements among hypothetical alternatives

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S ystemsAnalysis LaboratoryHelsinki University of Technology

– ARIADNE• Imprecision modelled by set inclusion; holistic

judgements among alternatives

– ISMAUT (White et al. 1984, Scherer et al. 1986):• Uncertainty about attribute weights and utilities,

exactly specified probabilities

• Hierarchical models:– RID (Moskowitz et al. 1989):

• Imprecise probabilities and utilities in decision trees

– MCRID (Moskowitz et al. 1991):• imprecise attribute weights; reduction of the set of non-

dominated alternatives via stochastic dominance

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S ystemsAnalysis LaboratoryHelsinki University of Technology

• AHP:– Saaty & Vargas (1987):

• Interval valued replies to pairwise comparisons suggested as a way to capture subjective uncertainty direct analysis of interval matrices intractable

– Arbel (1989):• Interval judgements interpreted as linear constraints

on local priorities

– Salo & Hämäläinen (1990):• Efficient decomposition scheme for processing

interval judgements in hierarchies

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PAIRS - Preference Assessment by Imprecise Ratio Statements

• Interval value tree analysis

• Pairwise ratio statements about the relative importance of attributes ( as intervals)

• Value intervals for the alternative scores (imprecition in value function and measurements combined in WINPRE)

• Inconsistency in pairwise statements not allowed

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S ystemsAnalysis LaboratoryHelsinki University of Technology

I Absolute : a dominates b if lower bound of the value interval for a is higher than upper bound of the value interval for b.

II Pairwise : a dominates b if there are no feasible weights, so that V(b) > V( a).

I => II , not II => I

Dominance

I

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S ystemsAnalysis LaboratoryHelsinki University of Technology

SPAIRS = Interval SMART/SWING

• Simple PAIRS : local comparisons made with respect to one reference attribute only

• Generalization:• Reference : most / least important or intermediate• No inconsistency problems ( because there are no

extra comparisons)• Easier to use than other interval methods.

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Interval AHP• Preference Programming term first used for

AHP (Arbel 1988)

• Pairwise comparisons with upper and lower limits for criteria and alternatives

• Inconsistency not allowed

• not a version of true AHP

• consistency must in elicitation

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S ystemsAnalysis LaboratoryHelsinki University of Technology

• DM gives preference statements, which define intervals of the weight ratios:

ijj

iij uw

wl

• Value intervals for alternatives: Series of LP - problems.

Preference programming

v a w v ai ii

n

( ) ( )

1

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S ystemsAnalysis LaboratoryHelsinki University of Technology

The feasible region• “The attribute X is at least two but no more

than four times as attractive as attribute Y”

yxy www 42 • Feasible region = the set of local priority

vectors which satisfy the inequalities arising from the interval judgements, i.e.

n

ijijijijiin wuwwlwwwwS

11 ,1,0),...,(

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Ambiguity Index• Index, which characterizes how specific the

DM’s preference statements are

nji ijij

ijij

lu

lu

nns

1 )~

1)(~1(

~~

)1(

2)(

• Properties

1,0)(

)()(S

ectorpriority v singlea of consists 0)(

compute easy to appealing,y Intuitivel

2121

S

SSS

SS

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Advantages of interval methods

• Partial progressively increasing information

• Allows ambiquity -all comparisons not necessary

• Group decision support– all opinions embedded into the interval

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S ystemsAnalysis LaboratoryHelsinki University of Technology

WINPRE• First to solve all interval methods • Efficient algorithm computes extreme points

instantaneously - sensitivity analysis• Maximum number of subcriteria or

alternatives is 9 • Number of levels in the value tree not limited • Results can be copied or linked to /from other

Windows programs (e.g. Excel)

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S ystemsAnalysis LaboratoryHelsinki University of Technology

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Value ratings on attributes

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S ystemsAnalysis LaboratoryHelsinki University of Technology

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S ystemsAnalysis LaboratoryHelsinki University of Technology

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S ystemsAnalysis LaboratoryHelsinki University of Technology

•SPAIRS with reference attribute in the middle

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S ystemsAnalysis LaboratoryHelsinki University of Technology

•SPAIRS with reference attribute the most important = SWING

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S ystemsAnalysis LaboratoryHelsinki University of Technology

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S ystemsAnalysis LaboratoryHelsinki University of Technology

•Interval AHP: pairwise comparison of attributes and alternatives

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S ystemsAnalysis LaboratoryHelsinki University of Technology

•Export of results into Excel

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Future research• Description of stuctured procedures based

on interval method

• Behavioural testing with real cases and decision makers-individual and group

• Winpre software is a fully operational DSS tool available free for research purposes:

• http://www.hut.fi/Units/Systems.Analysis

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S ystemsAnalysis LaboratoryHelsinki University of Technology

References

The underlying methodology of the program is described in the references below.

PAIRS

Salo and R.P. Hämäläinen: Preference assessment by imprecise ratio statements, Operations Research,

Vol. 40, No. 6, November-December 1992, pp. 1053-1061.

Preference Programming (INPRE-mode)

Salo and R.P. Hämäläinen: Preference programming through approximate ratio comparisons,

European Journal of Operational Research, Vol. 82, Issue 3, 1995, pp. 458-475.

Salo and R.P. Hämäläinen: Processing interval judgments in the analytic hierarchy process, Proc. of the Ninth

International Conference: Theory and Applications in Business, Industry and Government, in: Multipl Criteria

Decision Making, A. Goicocchea, L. Duckstein and S. Zionts (eds.), Springer-Verlag, New-York, August 1990,

Fairfax, Virginia, 1991, pp. 359-371.

Salo: Inconsistency analysis by approximately specified priorities, Mathematical and Computer Modelling,

Vol. 17, No. 4/5, 1993, pp. 123-133.

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Related articles

M. Pöyhönen and R.P. Hämäläinen: On the convergence of multiattribute weighting methods, Helsinki

University of Technology, Systems Analysis Laboratory Research Reports A69, October 1997.

(Available from http://www.hut.fi/Units/Systems.Analysis/Publications/)

M. Pöyhönen, R.P. Hämäläinen and A. A. Salo: An experiment on the numerical modeling of verbal ratio

statements, Journal of Multi-Criteria Decision Analysis, Vol. 6, 1997, pp. 1-10.

Salo and R.P. Hämäläinen: PRIME - Preference ratios in multiattribute evaluation, Helsinki University of

Technology, Systems Analysis Laboratory Research Reports A43, July 1992. (revised December 1997)

(Available from http://www.hut.fi/Units/Systems.Analysis/Publications/)

A. Salo and R.P. Hämäläinen: On the measurement of preferences in the analytic hierarchy process,

(and comments by V. Belton, E. Choo, T. Donegan, T. Gear, T. Saaty, B. Schoner, A. Stam, M. Weber,

B. Wedley) Journal of Multi-Criteria Decision Analysis, Vol. 6, 1997, pp. 309-339.

A. Salo and R.P. Hämäläinen: Rejoinder: The issue is understanding the weights, Journal of Multi-Criteria

Decision Analysis, Vol. 6, 1997, pp. 340-343

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S ystemsAnalysis LaboratoryHelsinki University of Technology

Applications, Group decisions

See the references below to get information about applications of the PAIRS and Preference Programming methods.

A. Salo: Interactive decision aiding for group decision support, European Journal of Operational Research,

Vol. 84, 1995, pp. 134-149.

R.P. Hämäläinen and O. Leikola: Spontaneous decision conferencing in parliamentary negotiations, Proc. of the

27th Hawaii International Conference on Systems Sciences, IEEE Computer Society Press, Hawaii, January 4-7,

Vol. IV, 1995, pp. 290-299.

R.P. Hämäläinen and O. Leikola: Spontaneous decision conferencing with top-level politicians, OR Insight,

Vol. 9, Issue 1, 1996, pp. 24-28.

R.P. Hämäläinen and M. Pöyhönen: On-line group decision support by preference programming in traffic planning,

Group Decision and Negotiation, Vol. 5, 1996, pp. 485-500.

R.P. Hämäläinen, A. Salo and K. Pöysti: Observation about consensus seeking in a multiple criteria environment,

Proc. of the Twenty-Fifth Hawaii International Conference on Systems Sciences, Hawaii, Vol. IV, January 1992, pp. 190-198.

R.P. Hämäläinen and E. Kettunen: On-line group decision support by HIPRE 3+ Group Link, Proc. of the 3rd

International Symposium on the Analytic Hierarchy Process, Washington, D.C., July 11-13, 1994, pp. 547-557

A. Salo and R.P. Hämäläinen: Decision support under ambigous preference statements, Proc. of the AIRO'90 Annual

conference of the Italian OR society, Sorrento, Italy, October 1990, pp. 229-243