The purpose of this paper is to perfect the axiom systems of buffer operator via adding the axiom of invariable trend.
Based on the three axioms of buffer operator, for any given data sequence of system behavior and any set of data satisfying the axiom of fixed point, it is proved that there always exists a buffer operator satisfying that the set of data is the buffer sequence of the given data sequence, and a specific constructor method of buffer operator is provided. Finally, the axiom of invariable trend is proposed to add in the axiom systems of buffer operator.
The results are convincing that although the raw sequence suffered from certain disturbance may be enlarged or reduced, the trend is in line with the original law. All predictions must be on the premise of this trend to forecast, or prediction will be considered invalid.
The method exposed in the paper can be used to construct a specific buffer operator between two sequences satisfying the axiom of fixed point.
The paper succeeds in providing a kind of universal constructor method for buffer operator, and adding the axiom of invariable trend to perfect the axiom systems of buffer operator and ensure the consistency of variation trend between the predicted values and the actual values.
Wei, Y., Kong, X. and Hu, D. (2011), "A kind of universal constructor method for buffer operators", Grey Systems: Theory and Application, Vol. 1 No. 2, pp. 178-185. https://doi.org/10.1108/20439371111163783
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