In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough sets and rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a class of revised...

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...

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...

Clustering is a standard approach in analysis of data and construction of separated similar groups. The most widely used robust soft clustering methods are fuzzy, rough and rough fuzzy clustering. The prominent feature of soft clustering leads to combine the rough and fuzzy sets. The Rough Fuzzy C-Means (RFCM) includes the lower and boundary estimation of rough sets, and fuzzy membership of fuz...

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relat...

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minim...

High dimensional microarray datasets are difficult to classify since they have many features with small number ofinstances and imbalanced distribution of classes. This paper proposes a filter-based feature selection method to improvethe classification performance of microarray datasets by selecting the significant features. Combining the concepts ofrough sets, weighted rough set, fuzzy rough se...

A fuzzy rough set approach has been proposed without using any fuzzy logical connectives. By this approach, gradual decision rules are induced from a given decision table. Fuzzy-rough modus ponens and fuzzy-rough modus tollens have been formulated based on the gradual decision rules. The equivalence condition between fuzzy-rough modus ponens and fuzzy-rough modus tollens is discussed. The condi...

Fuzzy sets and rough sets are known as uncertainty models. They are proposed to treat different aspects of uncertainty. Therefore, it is natural to combine them to build more powerful mathematical tools for treating problems under uncertainty. In this chapter, we describe the state of the art in the combinations of fuzzy and rough sets dividing into three parts. In the first part, we first desc...