Sequential three way decision with probabilistic rough sets
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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

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Sequential Three-way Decision with Probabilistic Rough Sets

Supervisor: Dr. Yiyu Yao

Speaker: Xiaofei Deng

18th Aug, 2011


  • 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


  • 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

  • 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

  • A task: selecting a set of relevant papers from a set of papers

  • A granular structure (with increasing evidence)

Basic concepts

  • An information table:

  • An equivalence relation

  • The equivalence class:

  • A partition,

Basic concepts (cont.)

  • A refinement-coarsening relation :

  • Suppose , we have the monotonic properties:

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 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 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 types of quantitative probabilistic decision rules:

  • Infer the membership in , based on the description of .

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.)

  • The lost function, for

  • A particular decision with the minimal risk

    • Considering the three regions

  • An example: the positive rule

Computing thresholds (cont.)

  • The pair of thresholds

    • For

    • We have:

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.)

  • 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

  • Step1: One single step three-way

  • Step i: refines the deferment rules in step (i-1)

(New universe)

(New concept)


  • 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

    • 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.


  • 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

Thank you.

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