Fundamenta Informaticae - Volume 148, issue 1-2

Authors: More, Anuj Kumar | Banerjee, Mohua

Article Type: Research Article

Abstract: Rough sets are investigated from the viewpoint of topos theory. Two categories RSC and ROUGH of rough sets and a subcategory ξ -RSC are focussed upon. It is shown that RSC and ROUGH are equivalent. Generalizations RSC (𝒞) and ξ -RSC(𝒞) are proposed over an arbitrary topos 𝒞. RSC(𝒞) is shown to be a quasitopos, while ξ -RSC(𝒞) forms a topos in the special case when 𝒞 is Boolean. An example of RSC(𝒞) is given, through which one is able to define monoid actions on rough sets. Next, the algebra of strong subobjects of an …object in RSC is studied using the notion of relative rough complementation. A class of contrapositionally complemented ‘c . ∨ c .’ lattices is obtained as a result, from the object class of RSC . Moreover, it is shown that such a class can also be obtained if the construction is generalized over an arbitrary Boolean algebra. Show more

Keywords: Rough sets, Elementary Topos, Quasitopos, Lattices with Complementation

DOI: 10.3233/FI-2016-1429

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 173-190, 2016

Authors: Düntsch, Ivo | Orłowska, Ewa | Wang, Hui

Article Type: Research Article

Abstract: In previous work we have presented a class of algebras enhanced with two contact relations representing rough set style approximations of a spatial contact relation. In this paper, we develop a class of relational systems which is mutually interpretable with that class of algebras, and we consider a relational logic whose semantics is determined by those relational systems. For this relational logic we construct a proof system in the spirit of Rasiowa-Sikorski, and we outline the proofs of its soundness and completeness.

DOI: 10.3233/FI-2016-1430

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 191-206, 2016

Authors: Chiaselotti, Giampiero | Ciucci, Davide | Gentile, Tommaso | Infusino, Federico

Article Type: Research Article

Abstract: We introduce and study new generalizations of some rough set tools. Namely, the extended core, the generalized discernibility function, the discernibility space and the maximum partitioner. All these concepts where firstly introduced during the application of rough set theory to graphs, here we show that they have an interesting and useful interpretation also in the general setting. Indeed, among other results, we prove that reducts can be computed in incremental polynomial time, we give some conditions in order that a partition coincides with an indiscernibility partition of a given information table and we give the conditions such that a discernibility …matrix corresponds to an information table. Show more

DOI: 10.3233/FI-2016-1431

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 207-227, 2016

Authors: Pancerz, Krzysztof

Article Type: Research Article

Abstract: The main goal of the paper is to show the idea of incorporating paradigmatic and syntagmatic relations into processing data stored in information tables using rough set methods. Input data, in a tabular form, are used in many machine learning and computational intelligence methods and algorithms, among others, those based on rough set theory. Additional knowledge about semantic relations (both paradigmatic and syntagmatic) can be considered as a useful context affecting data classification or clustering.

Keywords: information systems, rough sets, ontological graphs, semantic relations, paradigmatic relations, syntagmatic relations

DOI: 10.3233/FI-2016-1432

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 229-242, 2016