Multi-granulation Fuzzy Rough Sets Research Articles

Multi-granulation fuzzy rough sets

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 ...

Dynamic updating multigranulation fuzzy rough set: approximations and reducts

As we all known, dynamic updating of rough approximations and reducts are keys to the applications of the rough set theory in real data sets. In recent years, with respect to different requirements, many approaches have been proposed to study such problems. Nevertheless, few of the them are carried out under multigranulation fuzzy environment. To fill such gap, the updating computations of multigranulation fuzzy rough approximations are explored in this paper. By considering the dynamic increasing of fuzzy granular structures, which are induced by fuzzy relations, naive and fast algorithms are presented, respectively. Moreover, both naive and fast forward greedy algorithms are designed for granular structure selection in dynamic updating environment. Experiments on six data sets from UCI show that fast algorithms are more effective for reducing computational time in comparison with naive algorithms.

Intuitionistic fuzzy multigranulation rough sets

Exploring rough sets from the perspective of multigranulation represents a promising direction in rough set theory, where concepts are approximated by multiple granular structures represented by binary relations. Through a combination of multigranulation rough sets with intuitionistic fuzzy rough sets, this study develops a new multigranulation rough set model, called an intuitionistic fuzzy multigranulation rough set (IFMGRS). In the multigranulation framework, three types of IFMGRSs that are generalizations of three existing intuitionistic fuzzy rough set models are proposed. First, we present three types of IFMGRSs. From their basic properties, we conclude that they are extensions of three existing intuitionistic fuzzy rough sets. Second, we define the reducts of the three types of IFMGRSs to eliminate redundant intuitionistic fuzzy granulations. Third, we examine the reduction approaches of IFMGRS with a detailed example and discuss the general reduction theory of IFMGRS.

Multi-granulation fuzzy rough sets

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 fuzzy rough set models. Then it can be found that the Pawlak rough set model, fuzzy rough set model and multi-granulation rough set models are special cases of the new one from the perspective of the considered concepts and granular computing. The notion of rough measure and α, β-rough measure which are used to measure uncertainty in multi-granulation fuzzy rough sets are introduced and some basic properties of the measures are examined. The construction of the multi-granulation fuzzy rough set model is a meaningful contribution in the view of the generalization of the classical rough set model.

Robust Control, Optimization, and Applications to Markovian Jumping Systems

Robust Control, Optimization, and Applications to Markovian Jumping Systems

Multi-granulation Fuzzy Rough Sets in a Fuzzy Tolerance Approximation Space

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 upper approximations of a fuzzy set are defined on multiple fuzzy tolerance relations. It follows the research on the properties of the fuzzy lower and upper approximations of the new models. The fuzzy rough set model, rough set model on a tolerance relation and multi-granulation rough sets models are special cases of the new ones from the perspective of the considered concepts, related relations and granular computing. The new models are meaningful generalizations of the classical rough sets.