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Sequential Three-way Decision with Probabilistic Rough Sets. Supervisor: Dr. Yiyu Yao Speaker: Xiaofei Deng 18th Aug, 2011. Outline. Motivation The main idea Basic concepts and notations Multiple representations of objects in an information table

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sequential three way decision with probabilistic rough sets

Sequential Three-way Decision with Probabilistic Rough Sets

Supervisor: Dr. Yiyu Yao

Speaker: Xiaofei Deng

18th Aug, 2011

outline
Outline
  • Motivation
  • The main idea
  • Basic concepts and notations
  • Multiple representations of objects in an information table
  • Three-way decision with a set of attributes
  • Computation of thresholds
  • Sequential three-way decision-making with a sequence of attributes
motivation
Motivation
  • The three-way decision
    • One single step decision (current)
    • Minimal cost of correct, incorrect classifications (accuracy, misclassification errors)
  • Considering the cost of obtaining an evidence
    • Decision making: supporting evidence
    • An observation -> a piece of evidence
the main idea of sequential three way decision making
The main idea of sequential three-way decision making
  • Sequential model should consider the trade-off:
    • Cost Vs. misclassification error
  • The main idea of the sequential decision making
    • Selecting a sequence of evidence
    • Constructing a multi-level granular structure
    • For sufficient evidence,
      • Make an acceptance, rejection rules
      • Insufficient evidence: the deferment rules
    • For deferment rules,
      • Refining with further observation
the main idea cont an example
The main idea (cont.): An example
  • A task: selecting a set of relevant papers from a set of papers
  • A granular structure (with increasing evidence)
basic concepts
Basic concepts
  • An information table:
  • An equivalence relation
  • The equivalence class:
  • A partition,
basic concepts cont
Basic concepts (cont.)
  • A refinement-coarsening relation :
  • Suppose , we have the monotonic properties:
a short summary
A short summary
  • Based on the Information table
  • For two subsets of attributes:
    • With more details (supporting evidence)
  • The coarsening-refinement relation
    • Partial ordering between two partitions
    • Construct a granular structure
multiple representation of objects constructing a granular structure
Multiple representation of objectsConstructing a granular structure
  • The description of an object
    • (atomic formulas)
  • A sequence of sets of attributes:
    • (More evidence)
    • (Granules)
    • (Granulations)
  • A sequence of different descriptions of an object:
    • (Increasing details)
  • Construct a multi-level granular structure
    • With above elements
    • For sequential three-way decision
three way decision making with a set of attributes one single step three way decision making
Three-way decision making with a set of attributesOne single step three-way decision making
  • is an unknown concept
  • The Conditional probability:
  • The three probabilistic regions of
three way decision making cont
Three-way decision making (Cont.)
  • Three types of quantitative probabilistic decision rules:
  • Infer the membership in , based on the description of .
computation of the two thresholds
Computation of the two thresholds
  • Computing based on the Bayesian decision theory
    • A decision with the minimal risk
  • The cost of actions in different states
computing thresholds cont
Computing thresholds (cont.)
  • The lost function, for
  • A particular decision with the minimal risk
    • Considering the three regions
  • An example: the positive rule
computing thresholds cont1
Computing thresholds (cont.)
  • The pair of thresholds
    • For
    • We have:
sequential three way decision
Sequential three-way decision
  • A sequence of attributes
  • Non-Monotonicity
    • The new evidence
    • The conditional probability:
    • Support, is neutral, refutes
sequential three way decision cont
Sequential three-way decision (cont.)
  • Trade-off between Revisions and the tolerance of classification errors
    • Refine the deferment rules in the next lower level
    • Bias: making deferment rules
      • Higher , lower for a higher level
  • Conditions of thresholds:
an sequential algorithm
An sequential algorithm
  • Step1: One single step three-way
  • Step i: refines the deferment rules in step (i-1)

(New universe)

(New concept)

conclusion
Conclusion
  • Advantages
    • Consider cost of misclassification and the cost of obtaining an evidence
    • The tolerance of misclassification errors
    • Avoid test or observation to obtain new evidence at current level
    • Multi-representation of an object: an important direction in granular computing
  • Reports the preliminary results
future work
Future work
  • Future work
    • How to obtaining a sequence of attributes?
    • How to precisely measure the cost of obtaining the evidence for a decision?
    • A formal analysis of cost-accuracy trade-off to further justify the sequential three-way decision making.
reference
Reference
  • Yao, Y.Y., X.F. Deng, Sequential Three-way Decisions with Probabilistic Rough Sets, 10th IEEE International Conference on Cognitive Informatics and Cognitive Computing, 2011
slide21

Thank you.

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