We use covers of the universal set to de-ne approximation operators on the power set of the given set. In Section 1, we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets. We de-ne a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of t...

Article history: Received 24 February 2014 Received in revised form 12 June 2014 Accepted 24 July 2014 Available online 1 August 2014

Teoria mulţimilor rough, propusă de Zdzislaw Pawlak în anul 1982, reprezintă o tehnică utilă pentru analiza datelor incomplete. Ea are aplicaţii în diferite domenii, fiind considerată complementară altor teorii care lucrează cu astfel de date, cum sunt, de exemplu, teoria mulţimilor fuzzy sau inferenţa Bayesiană. Articolul prezintă câteva aplicaţii ale teoriei mulţimilor rough în domeniul elect...

This paper concerns a relationship between Bayes’ inference rule and decision rules from the rough set perspective. In statistical inference based on the Bayes’ rule it is assumed that some prior knowledge (prior probability) about some parameters without knowledge about the data is given first. Next the posterior probability is computed by employing the available data. The posterior probabilit...

Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang’s completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak’s the rough set theory. It is shown tha...

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 apply the rough set theory to BL-algebras. As a generalization of filters subalgebras of BL-algebras, we introduce the notion of rough filters subalgebras of BL-algebras and investigate some of their properties.

Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringb...

Many problems in real world can be explained in natural languages. Rough Set Theory is defined with many operations, rules extended from classical set theory and is widely used to model systems related to data mining. The paper is a description of Rough Set Theory and an illustration of modeling a real world problem based on Rough set approximations.

Dominance-based rough set introduced by Greco et al. is an extension of Pawlak’s classical rough set theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes satisfying upward and downward union properties. This paper introduces the concept of indexed blocks for representing dominance-based approximation spaces. Indexed ...