The principle of the minority subordinate to the majority is the most feasible and credible when people make decisions in real world. So generalized multigranulation rough set theory is a desirable fusion method, in which upper and lower approximations are approximated by granular structures satisfying a certain level of information. However, the relationship between a equivalence class and a c...

A type-2 computable real function is necessarily continuous; and this remains true for computations relative to any oracle. Conversely, by the Weierstrass Approximation Theorem, every continuous f : [0; 1]→ R is computable relative to some oracle. In their search for a similar topological characterization of relatively computable multi-valued functions f : [0; 1] ⇒ R (also known as multi-functi...

The probabilistic rough set (PRS) and the graded rough set (GRS) are two quantification models that measure relative and absolute quantitative information between the equivalence class and a basic concept, respectively. As a special PRS model, the decision-theoretic rough set (DTRS) mainly utilizes the conditional probability to express relative quantification. However, it ignores absolute quan...

Researchers from a wide variety of backgrounds and with a broad range of goals have utilized high-throughput screening technologies (i.e., microarray technologies) to identify candidate genes that may be associated with an observable characteristic or behavior (i.e., phenotype) of interest. However, the initial microarray analyses typically also yield many genes that are not related to the phen...

The DMU-package for Analyzing Multivariate Mixed Models has been developed over a period of more than 25 years. This paper gives an overview of new features and the recent developments around the DMU-package, including: Genomic prediction (SNPBLUP, G-BLUP and “One-Step”), Genome-wide association studies, Survival models and double hierarchical generalized linear mixed models.