A commentary on some of the intrinsic differences between grey systems and fuzzy systems

The aim of this paper is to distinguish between some of the more intrinsic differences that exist between grey system theory (GST) and fuzzy system theory (FST). There are several aspects of both paradigms that are closely related, it is precisely these close relations that will often result in a misunderstanding or misinterpretation. The subtly of the differences in some cases are difficult to perceive, hence why a definitive explanation is needed. This paper discusses the divergences and similarities between the interval-valued fuzzy set and grey set, interval and grey number; for both the standard and the generalised interpretation. A preference based analysis example is also put forward to demonstrate the alternative in perspectives that each approach adopts. It is believed that a better understanding of the differences will ultimately allow for a greater understanding of the ideology and mantras that the concepts themselves are built upon. By proxy, describing the divergences will also put forward the similarities. We believe that by providing an overview of the facets that each approach employs where confusion may arise, a thorough and more detailed explanation is the result. This paper places particular emphasis on grey system theory, describing the more intrinsic differences that sets it apart from the more established paradigm of fuzzy system theory.