Various expanded rough set models based on tolerance relations enlarge the application fields of rough set theory. Through generating tolerance relations to fuzzy tolerance relations and combining with dominance relations, a tolerance class of a fuzzy tolerance relation is further decomposed into a positive fuzzy tolerance class, a negative fuzzy tolerance class and a purely fuzzy tolerance cla...

Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract f...

In this paper, interactions among fuzzy, rough, and soft set theory has been studied. The authors have examined these theories as a problem solving tool in association rule mining problems of data mining and knowledge discovery in databases. Although fuzzy and rough set have been well studied areas and successfully applied in association rule mining problem, but soft set theory needs more atten...

Attribute selection is one of the important problems encountered in pattern recognition, machine learning, data mining, and bioinformatics. It refers to the problem of selecting those input attributes or features that are most effective to predict the sample categories. In this regard, rough set theory has been shown to be successful for selecting relevant and nonredundant attributes from a giv...

This paper generalizes the concepts of rough membership functions in pattern classification tasks to fuzz rough membership functions. Unlike the rough membersgp value of a pattern, which is sensitive only towards the rough uncertainty associated with the pattern, the fuzzy-rough membership value of the pattern signlfies the rou h uncertainty as well as the . fuzz uncertainty associated wig it. ...

Fuzzy rough sets, generalized from Pawlak’s rough sets, were introduced for dealing with continuous or fuzzy data. This model has been widely discussed and applied these years. It is shown that the model of fuzzy rough sets is sensitive to noisy samples, especially sensitive to mislabeled samples. As data are usually contaminated with noise in practice, a robust model is desirable. We introduce...

The problem of imperfect knowledge under uncertain environments has been tackled for a long time by philosophers, logicians and mathematicians. Rough set theory proposed by Zdzislaw Pawlak [1] has attracted attention of many researchers and practitioners all over the world, and has a fast growing group of researchers interested in this methodology. Fuzzy set theory proposed by Lotfi Zadeh [2] h...

Rough set theory is one of important tools of soft computing, and rough approximations are the essential elements in rough set models. However, the existing fuzzy rough set model for set-valued data, which is directly constructed based on a kind of similarity relation, fail to explicitly define fuzzy rough approximations. To solve this issue, in this paper, we propose two types of fuzzy rough a...

In this paper, a different approach to extract the threshold value β of Variable Precision Rough Set (VPRS) applied to continuous information systems is presented. This study combines the Fuzzy Set and Rough Fuzzy Set (RFS) theories to determine the β value of VPRS. The β value was determined by the Fuzzy C-means and relevant Fuzzy theories, for the reason that errors of system classification c...

This paper explores the implications of approximating a concept based on the Bayesian decision procedure, which provides a plausible unification of the fuzzy set and rough set approaches for approximating a concept. We show that if a given concept is approximated by one set, the same result given by the α-cut in the fuzzy set theory is obtained. On the other hand, if a given concept is approxim...