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The STP Model for Solving Imprecise Problems

The STP Model presents an innovative approach to solving imprecise problems characterized by fuzziness, uncertainty, and lack of clear structures. Unlike traditional models, which strive to clarify problems, the STP Model emphasizes exploring partially accurate solutions to manage complexity. It integrates a problem-solving space where varying degrees of solution feasibility are considered, relying on granular computing principles. This model serves as a guideline for researchers and practitioners to navigate the uncertainty inherent in many real-world problems, enabling a more adaptable problem-solving strategy.

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The STP Model for Solving Imprecise Problems

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  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)

  14. 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. 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

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