Fundamenta Informaticae - Volume 167, issue 3

Authors: Fajardo, William

Article Type: Research Article

Abstract: In this paper we present a computational package developed for making computations involved in many homological applications of the Grbner theory of skew PBW extensions.

Keywords: Noncommutative computational algebra, skew PBW extensions, Grbner bases, Maple, library SPBWE.lib

DOI: 10.3233/FI-2019-1813

Citation: Fundamenta Informaticae, vol. 167, no. 3, pp. 159-191, 2019

Authors: Michalak, Marcin | Ślęzak, Dominik

Article Type: Research Article

Abstract: Biclustering is considered as the method of finding two–dimensional subgroups in a matrix of scalars. The paper introduces a new approach to biclustering continuous matrices on the basis of boolean function analysis. We draw the strong relation between inclusion–maximal (maximal with respect to inclusion) biclusters of the assumed maximal difference between the data in a bicluster and prime implicants of a boolean function describing the data. These biclusters are called similarity biclusters. In the opposition to them, a new notion of dissimilarity biclusters was also introduced in the paper.

Keywords: bicluster, boolean reasoning, discernibility function, prime implicants, similarity biclusters, dissimilarity biclusters, continuous data biclustering

DOI: 10.3233/FI-2019-1814

Citation: Fundamenta Informaticae, vol. 167, no. 3, pp. 193-217, 2019

Authors: Rupnik Poklukar, Darja | Žerovnik, Janez

Article Type: Research Article

Abstract: Closeness is a measure of centrality, an important feature of communication and social networks. Extremal networks among all graphs and among several subclasses of graphs including trees and cacti are given. In addition, maximal graphs among cacti with fixed number of cycles and among cacti with given number of cut edges are provided.

Keywords: Closeness, graph operations, extremal graphs

DOI: 10.3233/FI-2019-1815

Citation: Fundamenta Informaticae, vol. 167, no. 3, pp. 219-234, 2019

Authors: Wasilewski, Piotr

Article Type: Research Article

Abstract: The paper is aimed at comparing Rough Set Theory (RST) and Formal Concept Analysis (FCA) with respect to algebraic structures of concepts appearing in both theories, namely algebras of definable sets and concept lattices. The paper presents also basic ideas and concepts of RST and FCA together with some set theoretical concepts connected with set spaces which can serve as a convenient platform for a comparison of RST and FCA. In the last section there are shown necessary and sufficient conditions for the fact, that families of definable sets and concept extents determined by the same formal contexts are equal …. This in finite cases is equivalent to an isomorphism of respective structures and generally reflects a very specific situation when both theories give the same conceptual hierarchies. Show more

Keywords: Rough Set, Rough Set Theory, Formal Concept, Formal Concept Analysis, Granular Set, Lattice

DOI: 10.3233/FI-2019-1816

Citation: Fundamenta Informaticae, vol. 167, no. 3, pp. 235-256, 2019