The STP Model for Solving Imprecise Problems

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

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 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 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. 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. STP Model (GrC'06)

6. A Research Question Hypotheses Hypotheses Verification An Example 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 ωєΩ in certain degree [0,1] STP Model (GrC'06)

8. Traditional Approach • Start from an impreciseω0 until a precise or solvable ωn. • < ω0,….,ωn>, ai= F(ωn) • ωj is a refinement ωi (i < j) STP Model (GrC'06)

9. The Diagram of STP Model A problem Representing problem Planning solutions Evaluating solutions Learning from the experience of solving 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) 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 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 ) = {aiє A | pi(a, ω0 ) > 0 } • At the step I • In practice 0 should be replaced by a threshold θ. STP Model (GrC'06)

13. STP Model (GrC'06)

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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. STP Model (GrC'06)

16. Conclusion • Imprecise is a nature of many problems. • Instead of clarify the problem, STP tries to approximatean imprecise problem by its solutions. • An application of systems thinking and granular computing. STP Model (GrC'06)

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