We develop two algebraic semantics for bitten rough set theory ([19]) over similarity spaces and their abstract granular versions. Connections with choice based generalized rough semantics developed in [15] by the present author and general cover based rough set theories are also considered.

The theory of generalized neighborhood system-based approximation operators plays an important role in the theory of generalized rough sets since it includes both the neighborhood-based approximation operators and the covering-based approximation operators as its special circumstances. The theory of reduction is one of the most significant directions in rough sets. In this work, the reduction o...

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

Rough set theory is an important technique for knowledge discovery in databases, and its algebraic structure is part of the foundation of rough set theory. In this paper, we present the structures of the lower and upper approximations based on arbitrary binary relations. Some existing results concerning the interpretation of belief functions in rough set backgrounds are also extended. Based on ...

Rough set theory is a relative new tool that deals with vagueness and uncertainty inherent in decision making. This paper introduce a new probabilistic approach for reducing dimensions and extracting rules of information systems using expert systems. The core of the approach is a soft hybrid induction system called the Generalized Distribution Table and Rough Set System (GDT-RS) for discovering...

Abs t rac t . Knowledge discovery in databases, or data mining, is an important objective in the development of dataand knowledge-base systems. An attributeoriented rough set method is developed for knowledge discovery in databases. The method integrates learning from example techniques with rough set theory. An attribute-oriented concept tree ascension technique is first applied in generalizat...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

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...

This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe. The concept of standard rough set algebras is generalized in two directions. One is based on the use of non-equivalence relations. The other is based on relations over two universes, which leads to the notion of interval algebras. Pawlak rough set algebras may be used to interpr...