http://orcid.org/0000-0002-5591-5967
![Sample our Economics, Finance,Business & Industry journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5931/TOC-Subject-Sample-2021-Economics-Finance-Business-Industry.jpg"})
ABSTRACT
Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. Once again, although and either of
and
are sufficient, we use
and both
and
for simplicity.
2. This set of axioms (A1)–(A5) is not the shortest possible. It can be simplified since some axioms are derived from others. However, this paper uses the convenient and conventional axioms to avoid mathematical difficulties.
3. Since the intersection can be obtained by means of the union
and the complement
such as
(or,
can be obtained by
and
such as
, vice versa), only one of
or
is required. However, for the sake of simplicity, it is common to define these three operations (
,
, and
) as the basic operations of Boolean algebra. The authors also ignore the so-called Sheffer stroke, written as
and named after Henry M. Sheffer, that can represent those basic operations using just one symbol. In logic, the Sheffer stroke symbolizes NAND calculus, defined by
, and leads to
,
, and
. In set theory, the Sheffer stroke is defined as
.
4. C is a set of C-fact types (called the coordination base), R is a set of C-fact types and P-fact types (called the response base), I is a set of C-fact types (called intention base), S is a set of C-fact types and P-fact types (called the state base), P is a partial function (called the performance function), D is the set of time durations, represents the power set of a set X, and then
.
5. In DEMO, a transaction and a transaction kind are distinguished, similar to an object (instance) and a class in an object-oriented programming language such as Java. A transaction kind is a template, similar to how a class is an extensible template with member variables (for representing state) and methods (or member functions; implementations of operation). For every execution, a transaction kind generates a new transaction as an instance of the transaction kind, similar to how a class generates a new object of the class.
6. Please note that operations defined in this step and those defined in Step 1 are not equivalent. The operations defined in this step are operations over (on) the algebra, whereas the operations defined in Step 1 are operations in the algebra i.e., specifications of the algebra.
7. Mathematically speaking, this structure should be defined with a many-sorted underlying set. However, in order to support understandability over mathematical rigidness, this article keeps the underlying set as a single-sorted set.
8. can be interpreted as the intention to restore some actor roles that are once deleted by
, but are still required by Condition 4 and Condition 5.
9. Well-formedness refers to the closedness, commutativity, and associativity as in (Enjo, Tanabu, and Iijima Citation2009).