The similarities and divergences between grey and fuzzy theory

Abstract

This article aims to provide the reader with a clearer understanding of the similarities and the divergences that exist between grey and fuzzy theory. The notion of fuzzy is considerably more established to that of grey, however, in recent years grey theory has garnered traction and has become more noticeable to wider audiences. Both can be seen as being proponents of uncertainty modelling, within their repertoires there are indeed facets that are similar in nature, and it is precisely these considerations that will often cause confusion. As grey theory generates more popularity, there will evidently be a need to address the issues regarding the similarities. The differences that exist in some cases are intrinsically subtle, hence the need for a definitive explanation. They are two distinctly separate paradigms, however, one could be forgiven for assuming that grey theory utilises fuzzy notions, simply presented with a different name. This article will aim to provide the reader with a coherent pairwise comparison of instances where similarities occur, describing the perspective adopted from both approaches. What will be covered will include the differences that exist between an interval-valued fuzzy set to that of a grey set; interval and grey numbers — both the discrete and the generalised grey number. Also highlighted will be the links to that of probability theory; imprecise and precise; belief and possibility functions. In describing the differences one will also gain an understanding of the similarities that indeed exist between the two.