Knowledge Representation and Validation in a Decision Support System: Introducing a Variability Modelling Technique - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 42

common choice/decision point that excludes this decision. The general form for describing a
dead decision is:
Decision A excludes decision B and decision A is common then decision B is a dead decision.
According to the proposed method, there are two possibilities for a decision: decision point
or choice, two possibilities for decision (A) to be common and three possibilities for the
exclusion.
Two possibilities for decision (A) to be common:
1. Common decision point:
∃ A :type(A, decisionpoint) ∧ common(A,yes).
2. Common choice belongs to common decision point:
∃ A,C:type(A, choice) ∧ type(C, decisionpoint) ∧ choiceof(C,A) ∧ common(C,yes) ∧ common(A,yes) .
Three possibilities for the exclusion constraint:
3. Choice excludes choice:
∃ A,B: type(A, choice) ∧ type(B, choice) ∧ excludes_c_c(A,B).
4. Choice excludes decision point:
∃ A,C :type(A,choice) ∧ type(C, decisionpoint) ∧ excludes_c_dp(A,C).
5. 5. Decision point excludes decision point:
∃ A,C: type(A, decisionpoint) ∧ type(C, decisio point) ∧ excludes_dp_dp(A,C).
If we apply the two possibilities of common decision to the three possibilities of the
exclusion constraint then we have six possibilities for satisfying the general form of the dead
decision. These possibilities are (1, 3),(1, 4),(1, 5),(2, 3),(2, 4),(2, 5). The possibilities (1, 3), (1,
4) and (2, 5) are excluded because decision A cannot be decision point and choice at the
same time. Therefore, all the possible scenarios for the dead decision are: (1, 5), (2, 3), (2, 4).
These scenarios are represented by the following rules:
i. ∀ A,B,C:type(A,decisionpoint) ∧ common(A,yes) ∧ type(C,decisionpoint) ∧ excludes_dp_dp(A,C) ∧
type(B,choice) ∧ choiceof(C ,B) ⟹ dead_ decision (B).
The decision point C in the above rule represents a dead decision point. All choices
belonging to a dead decision point are dead decisions.
ii. ∀ A,B,C:type(A,choice) ∧ type(C,decisionpoint) ∧ choiceof(C,A) ∧ common(C,yes) ∧ common(A,yes) ∧
type(B, choice) ∧ excludes_c_c(A,B) ⟹ dead_ decision(B).
iii. ∀ A,B,C,D:type(A,choice) ∧ type(C,decisionpoint) ∧ choiceof(C,A) ∧ common(C,yes) ∧ common(A,yes
) ∧ type(B,choice) ∧ type(D,decisionpoint) ∧ choiceof(D,B) ∧ excludes_c_dp(A,D) ⟹ dead_ decision
(B).
Rule (i) represents case (1, 5), rule (ii) represents case (2, 3) and rule (iii) represents case (2,
4). The decision point D in rule 3 represents a dead decision point. The choice B represents
all choices belonging to D .
5. Scalability testing
Scalability is approved as a key factor in measuring applicability of the techniques dealing
with variability modeling [23]. The output time is a measurement key for scalability. A
system considers scalable for specific problem if it can solve this problem in a reasonable
time.
In this section, we discuss the experiments, which are developed to test the scalability of the
proposed method.