Treating fuzziness in subjective evaluation data
Treating fuzziness in subjective evaluation data
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DOI：
10.1016/j.ins.2006.02.015
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
Y. Nakamori;M. Ryoke
中科院分区：
文献类型：
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作者：
Y. Nakamori;M. Ryoke
提出了一种处理主观评价数据模糊性的方法，并将其应用于主成分分析和对应分析中。在现有的方法中，或直接从它发展的技术中，模糊集是从数据空间上的某些观点定义的，并且统计模型的模糊参数是用线性规划或最小二乘法识别的。在本文中，我们试图映射到参数空间的评价数据的变化，同时保持尽可能多的信息，从而定义模糊集的参数空间。显然，可以使用所获得的模糊模型来从扩展原理中导出诸如主成分得分之类的东西。然而，对于使用扩展原理的模糊模型，可能性分布随着解释变量值的增加而扩展。这对于主观评价（例如5级评价）不一定有意义。而不是这样做，我们提出了一种方法，明确表示的评价的准确性，使用一定数量的矩阵，指定的模糊参数扩散的特征值。作为一个数值例子，我们提出了对当地环境的主观评价数据的分析。
This paper proposes a technique to deal with fuzziness in subjective evaluation data, and applies it to principal component analysis and correspondence analysis. In the existing method, or techniques developed directly from it, fuzzy sets are defined from some standpoint on a data space, and the fuzzy parameters of the statistical model are identified with linear programming or the method of least squares. In this paper, we try to map the variation in evaluation data into the parameter space while preserving information as much as possible, and thereby define fuzzy sets in the parameter space. Clearly, it is possible to use the obtained fuzzy model to derive things like the principal component scores from the extension principle. However, with a fuzzy model which uses the extension principle, the possibility distribution spreads out as the explanatory variable values increase. This does not necessarily make sense for subjective evaluations, such as a 5-level evaluation, for instance. Instead of doing so, we propose a method for explicitly expressing the vagueness of evaluation, using certain quantities related to the eigenvalues of a matrix which specifies the fuzzy parameter spread. As a numerical example, we present an analysis of subjective evaluation data on local environments.