Grey Clustering And Grey Target Decision-making Study

Grey System Theory and Fussy Set Theory are both efficient tools to deal with incomplete, imprecise and uncertain information. Absolutely, it is of great practical significance to study more efficient and general means to solve uncertain problems with the combination of these two theories.This article studies a number of effective researches for decision-making method and clustering algorithm based on the combination of grey system theory and fuzzy set theory. This paper establishes a similarity coefficient formula of interval grey number which combines the use of fuzzy equivalent clustering with the clustering of interval grey number, and expands the range of classical equivalent clustering algorithms from the legible number to the interval grey number. And this paper proposes absolute and relative off-target distance of discrete grey number, and establishes a decision-making algorithm for incomplete information system while the evaluating background is known. And the main results are as follows: Firstly, based on grey system theory and method, by the joint application of the basic idea of fuzzy equivalent clustering and the method of grey system theory, the similarity coefficient formula of interval grey number is established which lays the foundation for the grey dynamic cluster. Secondly, the clustering algorithm of interval grey number is proposed to overcome the limitations that the fuzzy equivalent clustering can not apply to the interval grey number. The range of classical equivalent clustering algorithms is expanded from the legible number to the interval grey number. And the subjectivity and limitations of GICD method is analyzed and simplified, and decision-making of interval grey number is made easier. Thirdly, based on grey system theory and method, put forward a discrete-grey-number evaluation method of upper and lower limits, and when the lower limit is equal to the upper limit, the evaluation value degrades into a white number. Then discuss that how to process the evaluation value by interval evaluation when the evaluation value is incomplete. Lastly, propose absolute and relative off-target distance of interval discrete grey number, which extends the classical grey target decision-making to the case of discrete grey numbers. And then establish a decision-making algorithm for incomplete information system while the evaluating background is known.