In this paper basic notions of the rough intuitionistic fuzzy set theory will be given. In fact the paper concerns a relationship between rough intuitionistic fuzzy sets and lattice theory. We shall introduce the notion of rough intuitionistic fuzzy lattice (resp rough intuitionistic fuzzy ideals). We also defined intuitionistic fuzzy rough set corresponding to a rough set and given conditions ...

Granular Computing (GrC) can be considered as a common name of theories, methodologies, techniques, and tools that make use of granules, i.e. groups, classes, or clusters of a universe, in the process of problems solving. Basic ideas of crisp information granulation have appeared in related fields, such as interval analysis, rough set theory, Dempster-Shafer theory of belief functions, cluster ...

New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (RST) and to represent rough semantics. The foundations of the theory also rely upon the axiomatic approach to granularity for all types of general RST recently developed by the...

Set-valued information systems are generalized models of single-valued information systems. In this paper, we propose two new relations for set-valued information systems. Based on these two relations, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation and knowledge granularity measure are defined in set-valued information systems, and some properties ...

Many real world problems deal with ordering of objects instead of classifying objects, although most of research in data analysis has been focused on the latter. One of the extensions of classical rough sets to take into account the ordering properties is dominance-based rough sets approach which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this p...

Binary information table, multi-valued table and set-valued are three kinds of systems often encountered in processing. For any system, we can induce different granular structures, then construct the corresponding rough set models. Generally speaking, for same models Pawlak set, covering multi-granulation be induced according to rules. These effective tools data mining This paper studies relati...

As two important expanded quantification rough set models, the probabilistic rough set (PRS) model and the graded rough set (GRS) model are used to measure relative quantitative information and absolute quantitative information between the equivalence classes and a basic concept, respectively. The decision-theoretic rough set (DTRS) model is a special case of PRS model which mainly utilizes the...