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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. [ABSTRACT FROM AUTHOR]

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minimize the effects of uncertainty in type-1 fuzzy logic systems. Existing definitions of type-2 fuzzy rough sets are based on vertical-slice or α -plane representations of type-2 fuzzy sets, and the granular structure of type-2 fuzzy rough sets has not been discussed. In this paper, a definition of type-2 fuzzy rough sets based on a wavy-slice representation of type-2 fuzzy sets is given. Then the concepts of granular type-2 fuzzy sets are proposed, and their properties are investigated. Finally, granular type-2 fuzzy sets are used to describe the granular structures of the lower and upper approximations of a type-2 fuzzy set, and an example of attribute reduction is given. [ABSTRACT FROM AUTHOR]