Reviewing crisp, fuzzy, grey and rough mathematical models

The aim of this paper is to investigate advantages of grey system theory. A lot of vague concepts like fuzzy sets, grey systems or rough sets has been proposed in the past. However, the unique concept of grey system theory, for example, it is useful under lack of data situation, is still unclear because a few articles discuss and deal with in real application. In this paper firstly numbers, membership functions, operations, crisp conversions and data pre-processing methods of each vague concept are summarized to review with several illustrations. Secondly the uniqueness of grey concept is discussed. It is found that the grey lattice operation and the nominal-the- better of grey generating are unique methods unlike fuzzy- based models or rough-based models. The unique concepts of grey system theory are ´interval data analysis´ and ´target-based data analysis´, which should add to the existing ones. Given data sets are analyzed strategically in grey system theory from these concepts.