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

Abstract

Abstract-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.

The Grey Ten-Element Analysis Method: A Novel Strategic Analysis Tool

“…In this paper, the fourth represented question is trying to find the most well-fit approach to formulate the uncertainty of the proposed method. In spite of the fact that grey systems theory has been exercised less than the fuzzy logic in the SWOT applications based on the literature reviewing, the grey systems theory is employed to achieve the fourth question's goal in accordance with the advantages and the characteristic it possesses, which makes it an ideal tool for the TEA method analysis [94][95][96]. In order to find the firm's strategic position in the market and determining the best strategies, the TEA method calculates the reflection of the environmental factors based on the changes of the firm's internal factors over time.…”

The similarities and divergences between grey and fuzzy theory

“…Grey sets utilise the concept of grey numbers, and considers the characteristic function values of a set as grey numbers. If a restriction is applied to the characteristic function values so that they are within the range of [0, 1], then grey sets can be seen as an extension to type-1 fuzzy sets Khuman et al, 2014). One current held assumption is that grey sets are equivalent to interval-valued fuzzy sets.…”

“…One current held assumption is that grey sets are equivalent to interval-valued fuzzy sets. However, this is only true when a grey number does not contain discrete data, and is instead perceived to act like that of an interval, therefore, it can be argued that a grey number is in fact a generalisation of an interval-valued fuzzy set Yang et al, 2014;Khuman et al, 2014). Without understanding the differences one would be forgiven for assuming that an interval-valued fuzzy set and a grey set are one and the same (Deschrijver and Kerre, 2003).…”

“…Section 3 notifies the reader to where these close relations lie, so one is able to better understand the nature of the inherent subtleties. Grey theory can be seen as an extension to fuzzy theory, or in certain instances a special interpretation of fuzzy theory (Khuman et al, 2014). Shedding light on where these instances occur, one is able to better understand the relationships that exist.…”

“…The underlying white number cannot be found between the values of (3, 7). If one was to employ an interval to capture the same scope [1, 10], one would have to also include (4, 6) as being possible candidates because an interval cannot exclusively disregard specific values from inside its own interval bounding (Khuman et al, 2014). If the grey number belonged to the candidate set g ± = [1, 10], then the values (4, 6) would be perfectly acceptable for both the grey number and the interval.…”