Aggregation Operators Ordered Weighted Average

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Aggregation OperatorsOrdered Weighted Average

• Mahdi Zarghaami
• Supervisor Dr. Reza Ardakanian
• Sharif University of Technology
• Sept. 2005

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Contents

• Aggregation Operators?
• OWA?
• Application
• New Extensions of OWA
• Extraction of the Weights
• Conclusion

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Aggregation of Inputs

• Data Modeling?
• Data Fusion?
• Application of Aggregation in Decision Making
  (MODM, MADM)
• Group Decision Making

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Aggregation Operator
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Multi-Attribute Decision Making

• Uncertainty in evaluations

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Aggregation Methods
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Weighted Aggregations
Ordered Weighted Average OWA Yager, 1988
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Why OWA?1-Continuous Transition from And to
ORto including aspiration level 2-Applicable in
Quantifier Guided Aggregations
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OWA and Other Operators

• Yager, 2004

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Applications

• Very Vast application in Science
• Vast application in Engineering
• Water Resources Management?

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The Aggregated Upper and Lower Probabilities for
Climate Change in year 2050Fu, Hall and Lawry
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MULTIPLE CRITERIA ANALYSIS FOR FLOOD VULNERABLE
AREAS, TurkeyYALÇIN, AKYÜREK
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Spatially variable risk perception in
GIS-baseddecision support systems,
UK.Makropoulos Butler(2005)
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Assessing vulnerability to earthquake hazards
through spatial multicriteria analysis of urban
areas, USA.RASHED WEEKS
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IDRISI (GIS Software)By varying the importance
of the factors in particular order positions, one
can adjust the levels of tradeoff between factors
and risk aversion in the solution incorporated
into the final model by OWA module
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Multiobjective optimization for sustainable
groundwater management in semiarid regionsMcPhee
Yeh, 2004
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Aggregation operators for soft decision making in
water resourcesDespic and Simonovic, 2000
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Extended OWA

• GOWA Generalized OWA
• HOWA Heavy OWA
• IOWA Induced OWA
• WOWA Weighted OWA
• LOWA Linguistic OWA

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Induced OWA

• Ui is order inducing variable (the importance of
  a criteria or an expert)

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OWA and its Measures
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Making Orness value (Alpha), Yager,1998

• Making Alpha by Rules

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1-Maximizing the Entropy OHagan Method
2-Minimizing the Variability Fuller Majlender
3-Minimizing the difference LP
Extracting the Weights
Parameterized Methods
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Learning the Weights from Data
Extracting the Weights
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Quantifiers
Extracting the Weights
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Quantifiers (cont.)
Extracting the Weights
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Quantifiers (cont.)
Extracting the Weights
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Which Method?

• Dependent on Data
• Dependent on Decision Makers Budget
• Dependent on Decision Makers Mind
• Dependent on Problem

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Conclusions

• OWA, a powerful method in aggregation
• We need a whole understanding of our problem.
• Models need more interaction by decision makers
• Data modeling in water management?!

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END