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...

Rough fuzzy sets are an effective mathematical analysis tool to deal with vagueness and uncertainty in the area of machine learning and decision analysis. Fuzzy information systems and fuzzy objective information systems exit in many applications and knowledge reduction in them can’t be implemented by reduction methods in Pawlak information systems. Therefore, this paper provides a model for ru...

Based on Pawlak’s two way approximations on Rough Sets and using thresholds G.Ganesan et al in 2004 proposed a method of rough indexing an information system which has fuzzy decision attributes. The limitation of Pawlak’s approximation is that it does not quantify the level of importance of the basic granules. Recently, Y.Y.Yao discussed Probabilistic Rough Set Model, which specified how basic ...

A hybrid unsupervised learning algorithm, termed as rough-fuzzy c-means, is proposed in this paper. It comprises a judicious integration of the principles of rough sets and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of ove...