不确定性原理的数据粒度
Data granulation by the principles of uncertainty
摘要：
粒建模的研究产生了各种数学模型，如区间，（高阶）模糊集，粗糙集和阴影集，这都是适合于描述所谓的信息粒。输入数据不确定性的建模是信息粒度化的一个重要方面。此外，不确定性在许多数学环境中是一个很好的研究概念，例如概率论，模糊集理论和可能性理论。这一事实表明，信息粒模型所表达的不确定性的适当量化可以用来定义一个不变的属性，在信息粒化的实际情况下加以利用。从这个角度来看，如果由合成的信息颗粒传达的不确定性与输入数据的不确定性呈单调递增关系，则信息颗粒化的过程是有效的。在本文中，我们提出了一个数据粒度框架，详细阐述了Klir引入的不确定性原则。作为系统和数据的介观描述符的不确定性，可以应用这些原理，而不管输入数据类型和信息颗粒所采用的特定数学设置。所提出的框架被认为是（i）提供一个指导方针的综合信息粒和（ii）建立一个基础，比较和定量判断不同的数据粒化过程。为了提供一个合适的案例研究，我们引入了一个新的数据粒度技术的基础上的最小距离和，这是专为生成2型模糊集。我们通过对两种不同的数据类型：特征向量和标记图进行不同的实验来分析该过程。结果表明，输入数据的不确定性是适当地传达所产生的第二类模糊集模型。
英文摘要：
Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.
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