module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

As a further extension of the fuzzy set and intuitive set, interval-valued (IIFS) is more effective tool to deal with uncertain problems. However, classical rough based on equivalence relation, which do not apply IIFS. In this paper, we combine IIFS ordered information system obtain (IIFOIS). On basis, three types multiple granulation models dominance relation are established effectively overco...

decision support systems (dsss) are prevalent information systems for decision making in many competitive business environments. in a dss, decision making process is intimately related to some factors which determine the quality of information systems and their related products. traditional approaches to data analysis usually cannot be implemented in sophisticated companies, where managers need...

decision support systems (dsss) are prevalent information systems for decision making in many competitive business environments. in a dss, decision making process is intimately related to some factors which determine the quality of information systems and their related products. traditional approaches to data analysis usually cannot be implemented in sophisticated companies, where managers nee...

Multidimensional scaling (MDS) is a statistical tool for constructing a low-dimension configuration to represent the relationships among objects. In order to extend the conventional MDS analysis to consider the situation of uncertainty under group decision making, in this paper the interval-valued data is considered to represent the dissimilarity matrix in MDS and the rough sets concept is used...

This paper proposes a new generalization of classical real-valued information systems, that is, interval-valued information systems. By defining an interval-valued dominance relation on a condition attribute, a rough set model and attribute reduction are established over interval-valued information systems. Moreover, several interesting properties are investigated by constructive approach. Furt...

The fuzzy rough set is a fuzzy generalization of the classical rough set. In the traditional fuzzy rough model, the set to be approximated is a fuzzy set. This paper deals with an incomplete fuzzy information system with interval-valued decision by means of generalizing the rough approximation of a fuzzy set to the rough approximation of an interval-valued fuzzy set. Since all condition attribu...

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. 

In the rough-set model, a set is represented by a pair of ordinary sets called the lower and upper approximations. In the interval-set model, a pair of sets is referred to as the lower and upper bounds which define a family of sets. A significant difference between these models lies in the definition and interpretation of their extended set-theoretic operators. The operators in the rough-set mo...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...