针对灰色定权聚类模型中白化权函数转折点只能为实数的情况,提出了当转折点为区间灰数时的白化权函数构造方法与计算过程。首先定义了区间灰数的标准化方法,将区间灰数的标准化形式带入实数型白化权函数,给出了区间灰数型白化权函数的表达式。然后分别对区间灰数型白化权函数中分段曲线只有一端为区间灰数和分段曲线两端均为区间灰数的情况进行讨论,得出两种情况下区间灰数型白化权函数值,并给出了区间灰数型典型白化权函数的四个转折点均为区间灰数的一般表达式。最后将该模型应用于许昌市民营企业核心竞争力的聚类评价中,取得了良好的结论。
As the society and economy developing, more and more problems need to use interval grey number. Aiming at the situation that the turn point of the whitenization function must be real number, the method of building and calculating the function when the turn point is an interval grey number was discussed in this paper. Firstly, this paper constructed weight function with interval gray number was constructed through defining the standardized methods of the interval grey number. Then use the standardized interval grey number replace the real number of the whitenization function. And the expression of the whitenization function with interval grey number was given. Secondly, discuss the two circumstances that there was only one interval grey number in the piecewise curve of the whitening function or two endpoints were both interval grey numbers. And when the four turn points were all interval grey numbers, the expression of whitenization function fjk(⊗) was given. At last, the interval grey clusters model was used to evaluate the core competencies of eight private enterprises in Xuchang. Our group had investigated the eight enterprises to get the data. And twenty experts had been asked to build the whitenization function. The result indicated the model is effective and reasonable.
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