1. The STP Model for Solving Imprecise Problems
JingTao Yao Wei-Ning Liu
Department of Computer Science
University of Regina

2. Nature Imprecise Problems
Problems are unclear, fuzzy, rough, or ill-structure
No suitable languages to present the problem.
The problem is not well-definable
J T Yao
STP Model (GrC'06)

3. Characteristics of Imprecise Problems
Multiple solutions and solution paths
Uncertainty about which concepts, rules and principles are necessary
Uncertainty about which solution is best
J T Yao
STP Model (GrC'06)

4. How to Solve Imprecise Problems?
Clarify the problem first.
Assumption: we are able to solve a clearly defined problem.
However, we may not be able to clarify an imprecise problem.
J T Yao
STP Model (GrC'06)

5. Solution-to-Problem Model
Explore partially accurate solutions to achieve manageability of problems.
An approximation process to problem.
Define a problem by its solutions.
Queries of search engines.
Research questions.
J T Yao
STP Model (GrC'06)

6. Hypotheses Verification
An Example
A Research Question
Hypotheses
Hypotheses Verification
J T Yao
STP Model (GrC'06)

7. Problem Solving Space (Ω, A, F)
Ω: problem domain,
A: the solution domain,
F: the solution function for the problems in Ω, F: Ω → 2A
Assuming each a є A is a solution of any ω є Ω in certain degree [0,1]
J T Yao
STP Model (GrC'06)

8. Traditional Approach
Start from an imprecise ω0 until a precise or solvable ωn.
< ω0,….,ωn>, ai= F(ωn)
ωj is a refinement ωi (i < j)
J T Yao
STP Model (GrC'06)

9. The Diagram of STP Model
A problem
Representing problem
Planning solutions
Evaluating solutions
Learning from the experience of solving
J T Yao
STP Model (GrC'06)

10. STP Approach
ω0 is defined by solutions <a0, …, an> where ai is a preferable solution than aj (i < j)
A solution ai is derived from ω0 and its previous solution ai-1.
ai = α (ai-1,ai-1)
J T Yao
STP Model (GrC'06)

11. The Representation of STP Model
The process of solving problem ω0 can be represented by a sequence of solutions:
<A0, …, Am>
Ai (0 < I < m) represents a set of possible solutions of the problem ω0
J T Yao
STP Model (GrC'06)

12. Potential Solution Nationhood and Potential Solutions Measure
In theory, any solution is a solution to any problem.
In practice, only some solutions are available and can be considered as solutions.
PNSi(ω0 ) = {ai є A | pi(a, ω0 ) > 0 }
At the step I
In practice 0 should be replaced by a threshold θ.
J T Yao
STP Model (GrC'06)

13. J T Yao
STP Model (GrC'06)

14. J T Yao
STP Model (GrC'06)

15. Granular Computing Way of Thinking
Divide and conquer, Top-down, and step-wise are three basic principles of GrC.
We may omit some exact and detailed information during information processing.
The STP model tries find the-best-so-far solution but not the-best-so-far-problem.
J T Yao
STP Model (GrC'06)

16. Conclusion Imprecise is a nature of many problems.
Instead of clarify the problem, STP tries to approximate an imprecise problem by its solutions.
An application of systems thinking and granular computing.
J T Yao
STP Model (GrC'06)

17. The STP Model for Solving Imprecise Problems
JingTao Yao Wei-Ning Liu
Department of Computer Science
University of Regina