Rough-DRSA: Rough extension of DRSA

Assumptions to verify

• •Class profiles or reference examples available in same uncertainty space
• •Linguistic categories map to Rough tuples

When not to use

• •No predefined classes

Worked example

1. 1.Step 1; Build decision table T: rows = examples, columns = condition criteria + 1 decision class column (e.g., low/medium/high).
2. 2.Step 2; For criteria set P ⊆ C, compute dominance: x D_P y ⟺ ∀q ∈ P: f(x,q) ≥ f(y,q) [or ≤ for min criteria]. Build P-dominating set D_P^+(x) and P-dominated set D_P^-(x) for each example.
3. 3.Step 3; Define class unions: upward Cl_t^≥ = ∪_{s≥t} Cl_s (e.g., 'medium or high'); downward Cl_t^≤ = ∪_{s≤t} Cl_s ('medium or low').
4. 4.Step 4; Compute P-lower approximation underline{P}(Cl_t^≥) = {x: D_P^+(x) ⊆ Cl_t^≥} (every x that dominates x is also in Cl_t^≥). Compute P-upper overline{P}(Cl_t^≥) = {x: D_P^-(x) ∩ Cl_t^≥ ≠ ∅}. Boundary BN = overline ∖ underline = inconsistent zone.
5. 5.Step 5; Quality of approximation γ_P = |∪_t underline{P}(Cl_t^≥)| / |U|. If γ_P = 1, P perfectly discriminates the classes.
6. 6.Step 6; Induce CERTAIN rules from lower approximations (form: ⋀ f(x,q) ≥ r_q ⇒ x ∈ Cl_t^≥). DOMLEM/VC-DomLEM find minimal cover. Kujawinska 2016 obtained 125 reliable rules from 866 records using VC-DomLEM, 4 attributes (Mn,Si,Ni,Cu).
7. 7.Step 7; Apply rule set to a new alternative: match premises, assign to class(es). Conflict-resolution (voting, strength, min-loss) if multiple rules trigger different classes. Evaluate via 10-fold cross validation accuracy + per-class sensitivity/precision (Kujawinska: 78% accuracy, sensitivity {0.95, 0.6, 0.56} for classes {1, 2, 3}).

Commonly paired with

• •n_a + ROUGH-DRSA (common)

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