Defining structures and grouping entities to provide solutions are known challenges that
have been studied by numerous researchers. In 1830, the French mathematician ?? Evariste Galoris
was the first to coin the term group theory, introducing the collective notion of entities.1 His
research on this subject was further developed in the nineteenth century by leading scientists such
as Augustin-Louis Cauchy, Sir Arthur Kayley, Camille Jordan, and others.2 They were mostly
concerned with inner association patterns of abstractions, membership of entities in defined groups,
and attribute commonalities. Moreover, these mathematicians were primarily occupied with the
contribution of groups to the relationship formations of entities, as expressed by Cassius J. Keyser
in his publication Mathematical Philosophy, A Study of Fate and Freedom in 1922. He indicated
that groups are instruments for defining, delimiting, discriminating, and classifying doctrines.3
Keyser not only elaborated on the capabilities of entity groups to serve as tools that can
be used to manipulate formations; he also provided an analysis mechanism that enables today??™s
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156 Ch. 8 Service-Oriented Analysis Modeling
practitioners to operate on software collections and manipulate their structures and processes for
the purpose of deriving analysis propositions. Here, the requirement is to address the selection
of service-oriented assets for a project and deal with service structures and processes.
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