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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. 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

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  1. Sequential Three-way Decision with Probabilistic Rough Sets Supervisor: Dr. Yiyu Yao Speaker: Xiaofei Deng 18th Aug, 2011

  2. 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

  3. 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

  4. 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

  5. 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)

  6. Basic concepts • An information table: • An equivalence relation • The equivalence class: • A partition,

  7. Basic concepts (cont.) • A refinement-coarsening relation : • Suppose , we have the monotonic properties:

  8. 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

  9. 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

  10. 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

  11. Three-way decision making (Cont.) • Three types of quantitative probabilistic decision rules: • Infer the membership in , based on the description of .

  12. 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

  13. Computing thresholds (cont.) • The lost function, for • A particular decision with the minimal risk • Considering the three regions • An example: the positive rule

  14. Computing thresholds (cont.) • The pair of thresholds • For • We have:

  15. Sequential three-way decision • A sequence of attributes • Non-Monotonicity • The new evidence • The conditional probability: • Support, is neutral, refutes

  16. 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:

  17. An sequential algorithm • Step1: One single step three-way • Step i: refines the deferment rules in step (i-1) (New universe) (New concept)

  18. 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

  19. 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.

  20. 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

  21. Thank you. Any Questions?

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