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...

Granular Computing has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules. Information granules are formalized within various frameworks such as sets (interval mathematics), fuzzy sets, rough sets, shadowed sets, probabilities (probability density functions), to name several the most visible approaches. In spite of the apparent diver...

In this paper, within the context of fuzzy rough set theory, we generalize the classical rough set framework for data-based attribute selection and reduction, based on the notion of fuzzy decision reducts. Experimental analysis confirms the potential of the approach.

We provide a new approach to synthesis of Formal Concept Analysis and Rough Set Theory. In this approach, the formal concept is considered to be a collection of objects accompanied with two collections of attributes—those which are shared by all the objects and those which are possessed by at least one of the objects. We define concept-forming operators for these concepts and describe their pro...

The main aim of this article is to compare the results of classical Shapley value concept with results of the Shapley value extended to the cooperative games with fuzzy coalitions applied on the real data of the cooperative simple game – in this case the data from the voting in the Lower House of the Czech Parliament 20022012. One of the most intriguing tasks is to describe real system problems...

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment. Firstly, based on the (α, β, γ)-cut relation R̃{(α,β,γ)}, we propose a rough set model in generalized single-valued neutrosophic approximation spaces. Then, some properties of the new rough set model are discussed. Furthermore, we obtai...

One of the many successful applications of rough set theory has been to the area of feature selection. The rough set ideology of using only the supplied data and no other information has many benefits, where most other methods require supplementary knowledge. Fuzzy-rough set theory has recently been proposed as an extension of this, in order to better handle the uncertainty present in real data...