Decision Support with Imprecise Data for Consumers

1
Decision Support with Imprecise Data for Consumers

• Gergely Lukacs
• lukacs_at_ipd.uni-karlsruhe.de
• Institute for Program Structures and Data
  Organisation
• Universtität Karlsruhe

2
Product Evaluations As of Today
Product labels (Energy Star)
Product evaluations (Which Magazine)
Web-metashopprice comparison
unbiased


--
professional
--


Usercommuni-cation
easy access
-
--

personalised
--
--

sophisticatedinformation
--


3
Evaluating Information Systems
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Energy Saving Climate Change Mitigation

• Source
• Intergovernmental Panel on Climate Change
  Climate Change 2001 Mitigation

• Negative costs!

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Imprecise Data inEvaluating Information Systems
Usage pattern
professional
Predictions (energy costs)
Product descriptions
Evaluating information system
Alternative database
Web-shop
electronic product label
classified advertisements
public transport timetable
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Background Imprecise Data
retail price energy consumption

• Precise value
• Imprecise value
• unknown (partial information ignored)
• possible values
• probability distribution
• imprecise probabilities
• probability- necessity measures, etc.

EUR
0
1000
NULL
EUR
0
1000
EUR
0
1000
Pr
EUR
0
1000
PrL
PrU
1000
0.1
0.6
900
0.7
900, 1000
0.8
1200
0.8
7
Background Decisions under Imprecise Data
Pr
Pr
?
EUR
EUR
0
1000
0
1000

• Decision theory (economic science)
• Expected value
• Alt1 gt Alt2 ? E(?1) lt E(?2)
• Bernoulli-principle
• Alt1 gt Alt2 ? Ec(?1) lt Ec(?2)
• Risk preference
• risk aversion, risk sympathy
• Height preference

8
Related Work
9
Background Imprecise data
Retail price energy consumption

• Precise value
• Imprecise value
• Unknown (partial information ignored)
• Possible values
• Probability distribution
• Imprecise probabilities
• Probability- necessity measures, etc.

EUR
0
1000
NULL
EUR
0
1000
EUR
0
1000
Pr
EUR
0
1000
PrL
PrU
1000
0.1
0.6
900
0.7
900, 1000
0.8
1200
0.8
10
Related Work

• Research general approaches for information
  systems, databases
• very complicated handling
• semantics
• Our approach
• Description of imprecise data
• Comparison/Sorting imprecise data
• (Joining imprecise data)

Evaluating information systems Decision theory
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Description of imprecise values

• Very high expressive power
• as much or as little information, as
  available
• Set of possible values
• Imprecise probabilities
• Random sets!

EUR
0
1000
PrL
PrU
1000
0.1
0.6
900
0.7
900, 1000
0.8
1200
0.8
12
Sorting (comparing) imprecise values

• Bernoulli principle
• cost function known
• precise probabilities
• Extended Bernoulli-principle
• possible values,imprecise probabilities
• Cost function unknown

Alt1 gt Alt2 ? Ec(?1) lt Ec(?2)
Alt1 gt Alt2 ? EUc(?1) lt EL c(?2)
Alt1 lt Alt2 ? ELc(?1) gt Eu c(?2)
Alt1 Alt2 ? all other cases
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Sorting (comparing) imprecise values
preferences no mathematical background limited
time
p-cut
p-cut value
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Modified description

• Expressive power unlimited
• extended Bernoulli-principle
• cost function
• unknown
• different from alternative to alternative
• Form simplified
• Set of possible values -gt interval
• Lower upper probs. for random sets -gt selected
  sets

EUR
EUR
0
1000
0
1000
PrL
PrU
PrL
PrU
1000
0.1
0.6
900
0
0.7
900
900, 1000
0.7
0.8
0.1
0.2
900, 1000
900, 1000, 1100
0.8
1
1200
0.8
15
Conclusions

• Evaluating information systems
• imprecise data
• Approach
• concentrating on important issues, operations
• decision theoretically correct
• rather than general extension of a data model
• Description
• possible values, probability theory
• complicated handling, interpretation

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Conclusions

• Sort operation
• basis Bernoulli-principle, but
• imprecisions more general
• cost function unknown
• extended Bernoulli-principle
• powerful description of imprecise values
• p-cuts
• cost function unknown
• Simplified description (expressive power not
  restricted)
• Outlook
• join operation