No abstract

Multigranulation rough set theory is one of the most effective tools for data analysis and mining in multicriteria information systems. Six types of covering-based multigranulation fuzzy rough set (CMFRS) models have been constructed through fuzzy β -neighborhoods or multigranulation fuzzy measures. However, it is often time-consuming to compute these CMFRS models with a large fuzzy covering using set representation approaches. Hence, presenting novel methods to compute them quickly is our motivation for this paper. In this article, we study the matrix representations of CMFRS models to save time in data processing. Firstly, some new matrices and matrix operations are proposed. Then, matrix representations of optimistic CMFRSs are presented. Moreover, matrix approaches for computing pessimistic CMFRSs are also proposed. Finally, some experiments are proposed to illustrate the effectiveness of our approaches.

A type of reducts in intuitionistic fuzzy (IF) β-coverings has been presented based on the union operation. But for some problems, there is no reducts in IF β-coverings according to this definition. That is to say, this notion has its boundedness. Therefore, we present the new type of reducts in IF β-coverings in this paper, and we call it type-2 reduct. Moreover, the type-2 reducts in IF β-covering approximation spaces are investigated while adding and removing some objects of the universe. Firstly, the notion of the type-2 reduct in an IF β-covering approximation space is presented. Then, some properties of type-2 reducts of IF β-coverings are investigated while adding and removing some objects.

In this paper, we introduce the fractional p-adic Hardy operators and its conjugate operators and obtain its optimal weak type estimates on the p-adic Lebesgue product spaces.

No abstract