A new decision model to solve the clustering dilemma

In the case that the conclusion of a comparison between the maximum components δ
i
^k
and δ
j
^k
of decision coefficient vector δ
i
and δ
j
conflicts with that of a full comparison between δ
i
and δ
j
integrating other components, a clustering dilemma occurs. Here we show a novel method to solve the existing clustering dilemma. We define both the weight vector of grey synthetic measure and the decision coefficient vector with grey synthetic measure at first. Then a novel two-stage decision model with the weight vector of grey synthetic measure and the decision coefficient vector with grey synthetic measure is put forward, and several functional weight vector grey synthetic measures are given. This method can effectively solve the clustering dilemma with maximum values and produce consistent results. At last, a practical evaluation and decision problem of the projects for subjects constructing of a university demonstrates the effectiveness of the proposed novel two stages decision model with grey synthetic measure.