Relating Two Domains via a Third: An Approach to Overcome Ambiguous Attributions Using Multiple Domain Matrices

Abstract

Design Structure Matrices (DSM) and Domain Mapping Matrices (DMM) are commonly used to model and analyze the relationships within one domain (DSM) or between two domains (DMM). Being assembled into one larger square matrix, having DSMs on its diagonal and DMMs in all other fields, a so-called Multiple Domain Matrix (MDM) is formed. When relating two domains using a DMM, a problem arises when the nature of one individual relationship between the two domains is to be described. Usually, this is modeled by annotating each relationship with the additional information, much like comments in spreadsheet software. This, however, is yet impossible if the relationships should be in matrix notation to allow for algorithmic matrix analyses. Equally, this way, the annotations are not accessible as elements of another matrix, e.g. as DSM. This paper suggests a generic principle to solve the described problem in a way consistent with the matrix methodology. It proposes an approach using MDM and is thereby able to unambiguously provide the nature of each relationship between the elements of two domains. As a DSM is a mere case of a DMM having two identical domains, the approach proposed can equally be used to enrich the relationships within a DSM.

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