Rough set theory is a new method that deals with vagueness and uncertainty emphasized in decision making. The theory provides a practical approach for extraction of valid rules fromdata.This paper discusses about rough sets and fuzzy rough sets with its applications in data mining that can handle uncertain and vague data so as to reach at meaningful conclusions.

The management of uncertainty in databases is necessary for real world applications, especially for systems involving spatial data such as geographic information systems. Rough and fuzzy sets are important techniques that can be used in various ways for modeling uncertainty in data and in spatial relationships between data entities. This chapter discusses various approaches involving rough and ...

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection o...

In this article we firstly summarize some notions on L−fuzzy sets, where L denotes a complete lattice. We then study a special case of L−fuzzy sets, namely the “intuitionistic fuzzy sets”. The importance of these sets comes from the fact that the negation is being defined independently from the fuzzy membership function. The latter implies both flexibility and effectiveness in fuzzy inference a...

One of the main obstacles facing current intelligent pattern recognition applications is that of dataset dimensionality. To enable these systems to be effective, a redundancy-removing step is usually carried out beforehand. Rough Set Theory (RST) has been used as such a dataset pre-processor with much success, however it is reliant upon a crisp dataset; important information may be lost as a re...

Although fuzzy support vector machine introduces the fuzzy membership degree in maximizing the margin and improves performance of classifier, it has not fully considered the position of training samples in the margin. In this paper, a double margin (rough margin) based fuzzy support vector machine (RFSVM) algorithm is presented by introducing rough set into fuzzy support vector machine. Firstly...

an orthogonal approach to the fuzzification of both multisets and hybridsets is presented. in particular, we introduce $l$-multi-fuzzy and$l$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. in addition, we study the properties ofthese structures. also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

Since data increases with time and space, many incremental rough based reduction techniques have been proposed. In these techniques, some focus on knowledge representation on the increasing data, some focus on inducing rules from the increasing data. Whereas there is less work on incremental feature selection (i.e., attribute reduction) from the increasing data, especially the increasing real v...

Feature selection benefits machine learning and knowledge acquisition, it usually resorts to various intelligent methodologies. Fuzzy rough sets act as a powerful platform of processing, they have introduced divergence measures generate an effective method feature selection, called FS-DD. However, Algorithm FS-DD still has advancement space, because its underlying dependency degree with absolut...

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...