The so-called measure of approximation quality plays an important role in many applications of rough set based data analysis. In this chapter, we provide an overview on various extensions of approximation quality based on rough-fuzzy and fuzzy-rough sets, along with highlighting their potential applications as well as future directions for research in the topic.

the purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

Every event has an extent in time, which is usually described by crisp time intervals. However, under some circumstances, temporal extents of events are imperfect, and therefore cannot be adequately modelled by crisp time intervals. Rough sets and fuzzy sets are two frequently used tools for representing imperfect temporal information. In this paper, we apply a two-dimensional representation of...

Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuz...

Current Research Information Systems (CRISs) usually contain large amounts of heterogeneous and distributed data, which makes finding specific information difficult for a user. It is in these cases that the concept of a personal search agent, proactively informing the user about newly available information, becomes more and more popular. But how can the agent know what is useful for the user if...

Some properties of Intuitionistic Fuzzy (IF) rough relational algebraic operators under an IF rough relational data model are investigated and illustrated using diabetes and heart disease databases. These properties are important and desirable for processing queries in an effective and efficient manner. Keywords— IF Set, Rough Set, IF Rough Relational Database, IF rough Relational Operators.

he theory of fuzzy sets was ntroduced by Zadeh [22] in 1965 as an attempt to study the vagueness and uncertainity in real world problems. A.Rosenfeld [16] applied the notion of fuzzy sets and introduced the notion of fuzzy subgroups in groups. Since then various classical algebraic systems have been fuzzified. The theory of rough sets introduced by Z.Pawlak [14] in 1982 is another independent m...

Ever since the first hybrid fuzzy rough set model was proposed in the early 1990’s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operati...

In this paper, we propose a nearest neighbour algorithm that uses the lower and upper approximations from fuzzy rough set theory in order to classify test objects, or predict their decision value. It is shown experimentally that our method outperforms other nearest neighbour approaches (classical, fuzzy and fuzzy-rough ones) and that it is competitive with leading classification and prediction ...

KEY WORDS Contextual spaces, context relation, contextual rough sets, elements of a contextual rough set, the counterpart of the axiom of extensionality. ABSTRACT This paper originates from the conceptions of rough sets presented by Pawlak (1982, 1992). It also refers to Ziarko's conception (1993) and the conceptions of Blizard's multisets (1989a, 1989b), Zadeh's fuzzy sets (1965), and the auth...