Q2. What have the authors contributed in "Three-way decisions with probabilistic rough sets" ?
This paper provides an analysis of three-way decision rules in the classical rough set model and the decision-theoretic rough set model.
Q3. What future works have the authors mentioned in the paper "Three-way decisions with probabilistic rough sets" ?
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.
Q4. What is the meaning of the set to be approximated?
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.
Q5. What is the loss function for determining the threshold parameters?
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.
Q6. What is the error rate of accepting a nonmember of C as a member of C?
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.
Q7. What is the tolerance level of errors in the classical rough set model?
Suppose that their tolerance level of errors is 10% and the probabilistic positive region defined by the entire set of attributes produces 5% errors.
Q8. What is the importance of model selec-tion criteria with a three-way?
Forster [3] considered the importance of model selec-tion criteria with a three-way decision: accept, reject or suspend judgment.
Q9. What is the reason why the negative rules are redundant?
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.
Q10. What is the definition of the decision-theoretic rough set model?
By expressing losses as functions of P (C) and P (Cc), one can derive the formulation from the decision-theoretic rough set model.
Q11. What is the importance of the decision-theoretic rough set model?
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.