Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and u...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...

Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy T–similarity relations are used to define the optimistic and pessimistic fu...

Although computers have come a long way since their invention, they are basically able to handle only crisp values at the hardware level. Unfortunately, the world we llve in consists of problems which fail to fall into this category, i.e. uncertainty is all too common. In this work, we look at a problem which involves uncertainty. To be specific we deal with attributes which are fuzzy sets. Und...

The roughness of a rough set arises from the existence of its boundary region. In such a boundary region, each object has a non-zero rough membership degree. When an object’s rough membership degree is regarded as its fuzzy membership degree, a rough set can induce a fuzzy set. This relationship motivates us to assert that there may exist some inherent relations between the roughness of a rough...

This paper generalizes the concept of rough membership functions in pattern classi$cation tasks to rough–fuzzy membership functions and rough–fuzzy ownership functions. Unlike the rough membership value of a pattern, which is sensitive only towards the rough uncertainty associated with the pattern, the rough–fuzzy membership (or ownership) value of the pattern signi$es the rough uncertainty as ...

Automata theory plays a key role in computational theory as many computational problems can be solved with its help. Formal grammar is a special type of automata designed for linguistic purposes. Formal grammar generates formal languages. Rough grammar and rough languages were introduced to incorporate the imprecision of real languages in formal languages. These languages have limitations on un...

With the arrival of the information age, information acquisition and communication have become more and more important in the field of information technology. This paper uses the concept of homomorphism as a basic tool to study the communication between fuzzy information systems. The concepts of consistent and compatible mappings with respect to fuzzy sets are firstly defined and their basic pr...

Based on analysis of Pawlak’s rough set model in the view of single equivalence relation and the theory of fuzzy set, associated with multi-granulation rough set models proposed by Qian, two types of new rough set models are constructed, which are multi-granulation fuzzy rough sets. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzz...