The STP Model for Solving Imprecise Problems

The STP Model for Solving Imprecise Problems

JingTao Yao Wei-Ning LiuDepartment of Computer Science

University of [email protected]

J T Yao STP Model (GrC'06) 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


Characteristics of Imprecise Problems

• Multiple solutions and solution paths

• Uncertainty about which concepts, rules and principles are necessary

• Uncertainty about which solution is best


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.


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.


An Example

A Research Question

Hypotheses

Hypotheses Verification


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]


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)


The Diagram of STP Model

A problem

Representing problem

Planning solutions

Evaluating solutions

Learning from the experience of solving


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)


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


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.


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.


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.

The STP Model for Solving Imprecise Problems

JingTao Yao Wei-Ning LiuDepartment of Computer Science

University of [email protected]

The STP Model for Solving Imprecise Problems

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