Abstract
The principle of justifiable granularity (PoJG) balances coverage and specificity to optimize information granularity. Although numerous studies have successfully formed information granules (IGs) using this principle, the stability of these IGs rarely receives attention. This paper analyzes the stability of such an IG’s modal, performance and upper or lower bound. First, we define some concepts to quantify the stability. Then, by the use of the binomial distribution, the central limit theorem and the union bound, we prove some theorems, which rely on several reasonable hypotheses and reveal the relations between the data size and the stability of the IG’s modal, performance and upper or lower bound. Furthermore, we put forward an algorithm built on the theorems to generate stable IGs by building data that have the proper size. Finally, we analyze its time complexity, applications and limitations. Experiments indicate the reliability of this algorithm when it is applied to several probability distributions and real datasets with a large scale of evidence.
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