The STP Model for Solving Imprecise Problems

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The STP Model for Solving Imprecise Problems

• JingTao Yao Wei-Ning Liu
• Department of Computer Science
• University of Regina
• jtyao_at_cs.uregina.ca

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Nature Imprecise Problems

• Problems are unclear, fuzzy, rough, or
  ill-structure
• No suitable languages to present the problem.
• The problem is not well-definable

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Characteristics of Imprecise Problems

• Multiple solutions and solution paths
• Uncertainty about which concepts, rules and
  principles are necessary
• Uncertainty about which solution is best

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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.

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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.

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An Example
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Problem Solving Space

• (O, A, F)
• O problem domain,
• A the solution domain,
• F the solution function for the problems in O,
  F O ? 2A
• Assuming each a ? A is a solution of any ? ? O in
  certain degree 0,1

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Traditional Approach

• Start from an imprecise ?0 until a precise or
  solvable ?n.
• lt ?0,.,?ngt, ai F(?n)
• ?j is a refinement ?i (i lt j)

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The Diagram of STP Model
A problem
Representing problem
Planning solutions
Evaluating solutions
Learning from the experience of solving
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STP Approach

• ?0 is defined by solutions lta0, , angt where ai
  is a preferable solution than aj (i lt j)
• A solution ai is derived from ?0 and its previous
  solution ai-1.
• ai a (ai-1,ai-1)

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The Representation of STP Model

• The process of solving problem ?0 can be
  represented by a sequence of solutions
• ltA0, , Amgt
• Ai (0 lt I lt m) represents a set of possible
  solutions of the problem ?0

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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(?0 ) ai ? A pi(a, ?0 ) gt 0
• At the step I
• In practice 0 should be replaced by a threshold
  ?.

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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.

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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.

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The STP Model for Solving Imprecise Problems

• JingTao Yao Wei-Ning Liu
• Department of Computer Science
• University of Regina
• jtyao_at_cs.uregina.ca