Study On The Grey Buffer Operators And Smoothness Of Buffer Sequence

In research of system science, because of the existence of disturbances and the limited level of awareness, people get information with some uncertain. Grey systems theory is mainly developed to study uncertaunties of "small samples" and "poor information". According to the impact of the grey system, this paper focuses on the problems of buffer operator’s structure and sequence of smoothness to improve Grey Buffer Operator’s System Theory and Grey System Theory as well as expend its application. The main research is as follows:(1) In practice, there is a kind of sequence that its increase(or decrease) rate of former part is relatively slow, but from the end time, the latest data x(n) presents fast growth(or decline) trend because the system are greatly caused by outside factors,and it is proved by qualitative analysis that the trend will last.For modeling of the sequence, novel strengthening buffer operators are put forward based on the prior using latest information, and the theorem are proved theoretically according to the axiomatic of buffer operators.(2) The relationship between regulation degree and smoothness of buffer operators is put forward. the regulation of the strengthening buffer operates smaller, the buffer sequence is smoother. the regulation of the weakening buffer operates bigger, the buffer sequence is smoother. Then the regulation degree and smoothness of some kinds of strengthening buffer operators and weakening buffer operators are compared and the theorem are proved strictly.(3) Based on the fact that monotonic function affects the functioning of buffer operator, researches were done on the smoothness of buffer sequence when the monotonic function changes. Theoretically, the relationship between different buffer operator processed by monotone function and smoothness of buffer operators is put forward. No matter whether strengthening buffer operator or weakening buffer operator, and no matter whether monotonic increasing or monotonic decreasing, the size of buffer operator remains as similar as the original one through the changing of monotonic function, while the smoothness of buffer sequence is exactly opposite with the original one. Both theoretical analysis and empirical tests show that theorems proposed in this thesis are correct.