A Method for Capturing and Reconciling Stakeholder Intentions Based on the Formal Concept Analysis - Intentional Perspectives on Information Systems Engineering - page 155

4 The Goal Lattice Model

4.1 FCA (Formal Concept Analysis)

FCA (Formal Concept Analysis) is a formal model based on the complete lattice
of formal concepts [ 8, 14, 17] . Here, a concept refers a pair of a set of objects of
common attributes and a set of related attributes.
In FCA, the concept lattice plays a key role to model the concepts. A con-
cept lattice is a complete lattice with the following order relation defined by the
subconcept-subconcept relation:

Definition 1: Order Relation

C1(A 1 ,B 1 ) ≤ C 2 ( A 2 ,B 2 )) iff A 1 ⊆ A 2 ( iff B 1 ⊇ B 2 ) (1)

Definition 2: Complete Lattice
A complete lattice is a lattice with the infimum and supremum under an order
relation defined by (1).
By the definition, the concept lattice is a structured subset of objects and
attributes under the order relation. Thus, the concept lattice can model a structural of
a system of objects in terms of a set of specific relations on attributes of the objects.
Thus, it may represent cognitive structure of real-world [ 15, 17] .
The concept lattice can be generated from a context table exemplified by Fig. 1(a)
and is represented with Hasse diagram , a lattice diagram used in FCA, illustrated in
Fig. 1(b).
A context table in Fig. 1(a) represents the relationship between objects, stake-
holders, in row and attributes, concerns of the stakeholders, in column as the
intersection, X , in the table. The context table can help to understand the rela-
tionships among stakeholders and their concerns. However, it is not possible to
hierarchically structure the relationships among stakeholders and concerns, which
is the major drawback of the table form, i.e. matrix formalism.
The concept lattice of Fig. 1(b) is generated from the context table of Fig. 1(a)
by tracing the relationships in the following manner.

1. Put the top concept, C 11 , including all objects at the top, ({Manger, IT Dep., End
User, Developer}, ϕ ), and the bottom concept, C 51 , including all the attributes at

, {Productivity, Cost, Technology, Usability}).
2. Identify the second concept, C 21 and C 22 , by adding one element of attribute
which is maximally shared by the elements of object, Productivity or Cost.
3. By repeating the step 2 along with the lattice of objects and attributes, then the
procedure terminates by reaching to the bottom concept.

the bottom, ( ϕ