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

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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

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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

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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

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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)

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

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

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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

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Multiple representation of objects Constructing 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

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Three-way decision making with a set of attributes One single step three-way decision making is an unknown concept The Conditional probability: The three probabilistic regions of

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

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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 States Action

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

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

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

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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:

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

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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

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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.

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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

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