A mathematical framework for enterprise architecture representation and design

This paper presents a new mathematical framework for the representation and design of enterprise information architectures (EIA), also known as simply enterprise architectures (EA). Set theory is used to represent an EA as an 8-tuple consisting of a set of requirements, a set of business processes, a set of business systems, a set of data elements, a set of applications, a set of technologies, a set of constraints and business rules, and a set of architectural metrics and their values. These sets are then used to represent their respective architectural views, i.e. the Business Process Architectural View, the Business Systems Architectural View, etc. Next, it is shown that these multiple architectural views are all subsets of the same design point in the resource space. Design considerations leading to a Pareto efficient design point are discussed. Finally, the concept of Pareto design optimality is illustrated with one example in aircraft design and one example in database design.