Three-way decisions with probabilistic rough sets

Question

1. What can be used in interpreting the required parameters of three-way decision rules?

2. What have the authors contributed in "Three-way decisions with probabilistic rough sets" ?

3. What future works have the authors mentioned in the paper "Three-way decisions with probabilistic rough sets" ?

4. What is the meaning of the set to be approximated?

Accepted Answer

Ideas from hypothesis testing in statistics may be used in interpreting the required parameters involved in three-way decision rules.

Accepted Answer

This paper provides an analysis of three-way decision rules in the classical rough set model and the decision-theoretic rough set model.

Accepted Answer

Therefore, as future research, the authors need to reexamine and re-interpret notions from the classical rough model in the new probabilistic setting of three-way decisions.

Accepted Answer

The set to be approximated corresponds to a hypothesis and an equivalence class to a piece of evidence; the three regions correspond to the results of a three-way decision that the hypothesis is verified positively, negatively, or undecidedly based on the evidence.

Accepted Answer

The reverse order of losses is used for classifying an object not in C. Under condition (c0), the decision rules can be re-expressed as:(P) If Pr(C|[x]) ≥ α and Pr(C|[x]) ≥ γ, decide x ∈ POS(C); (B) If Pr(C|[x]) ≤ α and Pr(C|[x]) ≥ β, decide x ∈ BND(C); (N) If Pr(C|[x]) ≤ β and Pr(C|[x]) ≤ γ, decide x ∈ NEG(C);where the parameters α, β, and γ are defined as:α= (λPN − λBN)(λPN − λBN) + (λBP − λPP ) ,β= (λBN − λNN)(λBN − λNN) + (λNP − λBP ) ,γ= (λPN − λNN)(λPN − λNN) + (λNP − λPP ) . (8)In other words, from a loss function one can systematically determine the required threshold parameters.

Accepted Answer

For positive rules, the error rate of accepting a nonmember of C as a member of C is defined by Pr(Cc|[x]) = 1−Pr(C|[x]) = 1−c and is below 1−α.

Accepted Answer

Suppose that their tolerance level of errors is 10% and the probabilistic positive region defined by the entire set of attributes produces 5% errors.

Accepted Answer

Forster [3] considered the importance of model selec-tion criteria with a three-way decision: accept, reject or suspend judgment.

Accepted Answer

Based on the fact that the negative region can be expressed as NEG(C) = (POS(C) ∪ BND(C))c, the negative rules seem to be redundant.

Accepted Answer

By expressing losses as functions of P (C) and P (Cc), one can derive the formulation from the decision-theoretic rough set model.

Accepted Answer

When such an idea is applied to rough set theory, the authors need to introduce confidence levels of acceptance, abstaining, and rejection in the three-way decision making.

Three-way decisions with probabilistic rough sets

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Most frequently asked questions

1. What can be used in interpreting the required parameters of three-way decision rules?

2. What have the authors contributed in "Three-way decisions with probabilistic rough sets" ?

3. What future works have the authors mentioned in the paper "Three-way decisions with probabilistic rough sets" ?

4. What is the meaning of the set to be approximated?

5. What is the loss function for determining the threshold parameters?

6. What is the error rate of accepting a nonmember of C as a member of C?

7. What is the tolerance level of errors in the classical rough set model?

8. What is the importance of model selec-tion criteria with a three-way?

9. What is the reason why the negative rules are redundant?

10. What is the definition of the decision-theoretic rough set model?

11. What is the importance of the decision-theoretic rough set model?

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Citations

The superiority of three-way decisions in probabilistic rough set models

An Outline of a Theory of Three-Way Decisions

Three-way decision and granular computing

Three-Way Decisions and Cognitive Computing

Rough sets and current trends in computing: proceedings of the 8th international conference

References

Pattern Classification and Scene Analysis.

Pattern Classification and Scene Analysis

Rough Sets: Theoretical Aspects of Reasoning about Data

Rough sets

Pattern classification and scene analysis

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