1. Rough Set Model Selection for Practical Decision Making
Jeseph P. Herbert JingTao Yao
Department of Computer Science
University of Regina

2. Introduction
Rough sets have been applied to many areas in order to aid decision making.
Information (rules) derived from multi-attribute data helps users in making decisions.
Rough set reducts minimize the strain on the user by giving them only the necessary information.
J T Yao

3. Motivation
Can we further utilize the strengths provided by rough sets in order to make more informed decisions?
Can we differentiate the types of decisions that can be made from using various rough set methods?
Can we provide some sort of support mechanism to the user to help them choose a suitable rough set method for their analysis?
J T Yao

4. Rough Sets Developed in the early 1980s by Zdzislaw Pawlak.
Sets derived from imperfect, imprecise, and incomplete data may not be able to be precisely defined.
Sets must be approximated
Using describable concepts to approximate known concept
1.76 cm => 1.7, 1.8
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5. Information systems/tables and decision tables. Indiscernibility.
Key Concepts
Information systems/tables and decision tables.
Indiscernibility.
Set approximation.
Reducts.
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6. Information Table: An Example
I = (U, A)
U = non-empty finite set of objects
A = non-empty finite set of attributes such that:
for all
Object
Date
High
Close 1
1-Jul-91 2
2-Jul-91 3
3-Jul-91
is the set of value for attribute a.
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7. Decision Table: An Example
T = (U, A {d})
Object
Date
High
Close
Decision 1
1-Jul-91 2
2-Jul-91 3
3-Jul-91 -1
U = non-empty finite set of objects.
A = non-empty finite set of conditional attributes.
d = one or more decision attributes.
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8. Indiscernibility
For any in I = ( ), there exists an equivalence relation:
where is the B-indiscernibility relation.
An equivalence relation partitions U into equivalence classes:
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9. Set Approximation Data may not precisely define distinct, crisp sets.
A rough set has a lower and upper approximation.
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10. Visualize Rough Sets Let T = (U, A), , Lower Approximation:
Upper Approximation:
Boundary Region:
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11. Rough Set Methods for Data Analysis
Two type of models are focused on:
Algebraic Method
Probabilistic
Decision-theoretic Method,
Variable-precision Method
Each method has different strengths that can be used to improve decision making
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12. Types of Decisions
Broadly, there are two main types of decisions that can be made using rough set analysis.
Immediate decisions (Unambiguous).
Delayed decisions (Ambiguous).
We can further categorize decision types by looking at rough set method strengths.
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13. Immediate Decisions
These types of decisions are based upon classification with the POS and NEG regions.
The user can interpret findings as:
Classification into POS regions can be considered a “yes” answer.
Classification into NEG regions can be considered a “no” answer
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14. Delayed Decisions
These types of decisions are based on classification in the BND region.
A “wait-and-see” approach to decision making.
A decision-maker can decrease ambiguity with the following:
Obtain more information (more data).
A decreased tolerance for acceptable loss (decision-theoretic) or user thresholds (variable-precision).
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15. Algebraic Decisions Decisions made from algebraic rough set analysis.
Immediate
If P(A|[x]) = 1, then x is in POS(A).
If P(A|[x]) = 0, then x is in NEG(A).
Delayed
If 0 < P(A|[x]) < 1, then x is in BND(A).
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16. Variable-Precision Decisions
Decisions made from variable-precision rough set analysis.
User-defined thresholds u and l representing lower and upper bounds to define regions.
Pure Immediate decisions.
User-Accepted Immediate decisions.
User-Rejected Immediate decisions.
Delayed decisions.
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17. Variable-Precision Decisions
Pure Immediate
If P(A|[x]) = 1, then x is in POS1 (A).
If P(A|[x]) = 0, then x is in NEG0 (A).
User-Accepted Immediate
If u ≤ P(A|[x]) < 1, then x is in POSu (A).
User-Rejected Immediate
If 0 < P(A|[x]) ≤ l, then x is in NEGl (A).
Delayed
If l < P(A|[x]) < u, then x is in BNDl,u (A).
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18. Decision-Theoretic Decisions
Decisions made from decision-theoretic rough set analysis.
Calculated cost (risk) using Bayesian decision procedure provides minimum α, β values for region division.
Pure Immediate decisions.
Accepted Loss Immediate decisions.
Rejected Loss Immediate decisions.
Delayed decisions.
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19. Decision-Theoretic Decisions
Pure Immediate
If P(A|[x]) = 1, then x is in POS1 (A).
If P(A|[x]) = 0, then x is in NEG0 (A).
Accepted Loss Immediate
If α ≤ P(A|[x]) < 1, then x is in POSα (A).
User-Rejected Immediate
If 0 < P(A|[x]) ≤ β, then x is in NEGβ (A).
Delayed
If β < P(A|[x]) < α, then x is in BNDα, β (A).
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20. A Simple Example: Parking a Car
Set of states:
: meeting will be over in less than 2 hours,
: meeting will be over in more than 2 hours.
Set of actions:
: park the car on meter
: park the car on parking lot
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21. Costs of Parking Your Car
(meter)
(lot)
(<= 2)
$2.00
$7.00
(> 2)
$12.00
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22. Making Decision Based on Probabilities
Assume that:
Cost of each action:
Take action : park the car on meter
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23. Determine the Probability Threshold for One Action
The condition of taking action : park the car on meter:
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24. Relationships Amongst Rough Set Models
Decision-theoretic
model
Variable-precision
model
Probabilistic
rough set
approximations
Loss
function
Threshold
values
Baysian
decision
theory
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25. Summary of Decisions POS1 (A) POS(A) BND(A) POSu (A) BNDl,u (A) NEG(A)
Region
Decision Type
POS1 (A)
Pure Immediate
POSu (A)
User-accepted Immediate
BNDl,u (A)
Delayed
NEGl (A)
User-rejected Immediate
NEG0 (A)
Region
Decision Type
POS(A)
Immediate
BND(A)
Delayed
NEG(A)
Pawlak Method
Region
Decision Type
POS1 (A)
Pure Immediate
POSα (A)
Accepted Loss Immediate
BNDα, β (A)
Delayed
NEGβ (A)
Rejected Loss Immediate
NEG0 (A)
Variable-Precision Method
Decision-Theoretic Method
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26. Choosing a Method
If the user is informed enough to provide thresholds, variable-precision rough sets can be used for data analysis.
If cost or risk information is beneficial to the types of decisions being made, decision-theoretic rough sets can be used for data analysis.
J T Yao

27. Conclusions
We can utilize the strengths of various rough set methods in order to improve our decision making capability.
The various rough set methods can each make different types of decisions.
By determining what kind of decisions they wish to make, users can choose a suitable rough set method for data analysis to reach their goals.
J T Yao

28. Rough Set Model Selection for Practical Decision Making
Jeseph P. Herbert JingTao Yao
Department of Computer Science
University of Regina

29. Where is Regina?
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