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 38

selected (assigned by select predicate (select(x)) and x requires the choice y . Then the system
automatically assigns y by select predicate (select(y)). That means y is selected also. At the
end, select and not notselect predicates represent the selections of decision-making process.
Table 3 shows the main rules in our proposed method. The proposed method contains
thirteen main rules to validate the decision-making process. Rules 1 through 6 are used to
validate constraint dependency rules. Rules 7 and 8 deal with relationships between
decision point and their choice(s). Rules 10 and 11 satisfy the common property of decision
points and choices. Rules 12 and 13 validate the maximum and minimum property of
decision points. Appendix 1 describes the proposed rules in details.
4.1.2 Propagation and delete-cascade
This operation defines how some choices are selected automatically as a reaction to previous
selection of other choices.
Definition 1: Selection of the choice n , select(n) , is propagated from selection of the choice x ,
select(x) , in three cases:
i. ∀ x,y,z,n:type(x,choice) ∧ choiceof(y,x) ∧ select(x) ∧ requires_dp_dp(y,z) ∧ type(n,choice) ∧ choiceof(z,
n) ∧ common(n,yes) ⟹ select(n).
If x is a choice and x belongs to the decision point y and x is selected, that means y is selected
(rule 7), and the decision point y requires a decision point z , that means z is also selected
(rule 5), and the choice n belongs to the decision point z and the choice n is common. It
means the choice n is selected (rule 10).
ii. ∀ x,n: type(x,choice) ∧ type(n,choice) ∧ select(x) ∧ requires_c_c(x,n) ⟹ select(n).
If the choice x is selected and it requires the choice n , it means the choice n is selected, (rule
1). The selection of choice n propagated from the selection of x .
iii. ∀ x,z,n:type(x,choice) ∧ select(x) ∧ type(z,decisionpoint) ∧ requires_c_dp(x,z) ∧ type(n,choice) ∧ choiceof(
z,n) ∧ common(n) ⟹ select(n).
If the choice x is selected and it requires the decision point z, that means the decision point z
is selected (rule 3), and the choice n is common and belongs to the decision point z and that
means the choice n is selected (rule 10). The selection of the choice n is propagated from the
selection of x .
Delete-cascade operation
This operation validates the automated decision-making process during execution time. The
following scenario describes the problem:
If choice x is selected in time N and the two choices y and k are propagated due to selection
of x , then the decision list (at time N ) = { x , y , k }. In time ( N + 1), the choice m is selected, and
m excludes x , then x is removed from the decision list. The decision list at time ( N + 1) = { m ,
y , k }. The presence of the choices y and k is not correct. The choices y and k are not decision
maker's choices. The following rule implements the delete-cascade operation.
∀ x,y:type(x,choice) ∧ type(y,choice) ∧ requires_c_c(y,x) ∧ select(x) ∧ notselect(y) ⟹ notselect(x).
For all choices x , and y ; if the choice y requires x and x is selected and y is assigned by
notselect predicate, that means y is excluded in the configuration process, and x was selected
according to selection of y (y requires x) , then the presence of x after exclusion of y is not true.
The output for this operation is the assignment of the choice x with notselect predicate. This
assignment permits the proposed method to perform delete-cascade operation to verify the
selections.