Rough action on topological rough groups

[EN] In this paper we explore the interrelations between rough set theory and group theory. To this end, we first define a topological rough group homomorphism and its kernel. Moreover, we introduce rough action and topological rough group homeomorphisms, providing several examples. Next, we combine these two notions in order to define topological rough homogeneous spaces, discussing results concerning open subsets in topological rough groups.The authors wish to thank the Deanship for Scientific Research (DSR) at King Abdulaziz University for financially funding this project under grant no. KEP-PhD-2-130-39. Also, we would like to thank the editor and referees for their valuable suggestions which have improved the presentation of the paper.Altassan, A.; Alharbi, N.; Aydi, H.; Özel, C. (2020). Rough action on topological rough groups. Applied General Topology. 21(2):295-304. https://doi.org/10.4995/agt.2020.13156OJS295304212S. Akduman, E. Zeliha, A. Zemci and S. 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A cholesky-based SGM-MLFMM for stochastic full-wave problems described by correlated random variables

In this letter, the multilevel fast multipole method (MLFMM) is combined with the polynomial chaos expansion (PCE)-based stochastic Galerkin method (SGM) to stochastically model scatterers with geometrical variations that need to be described by a set of correlated random variables (RVs). It is demonstrated how Cholesky decomposition is the appropriate choice for the RVs transformation, leading to an efficient SGM-MLFMM algorithm. The novel method is applied to the uncertainty quantification of the currents induced on a rough surface, being a classic example of a scatterer described by means of correlated RVs, and the results clearly demonstrate its superiority compared to the non-intrusive PCE methods and to the standard Monte Carlo method

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Taming Wild High Dimensional Text Data with a Fuzzy Lash

The bag of words (BOW) represents a corpus in a matrix whose elements are the frequency of words. However, each row in the matrix is a very high-dimensional sparse vector. Dimension reduction (DR) is a popular method to address sparsity and high-dimensionality issues. Among different strategies to develop DR method, Unsupervised Feature Transformation (UFT) is a popular strategy to map all words on a new basis to represent BOW. The recent increase of text data and its challenges imply that DR area still needs new perspectives. Although a wide range of methods based on the UFT strategy has been developed, the fuzzy approach has not been considered for DR based on this strategy. This research investigates the application of fuzzy clustering as a DR method based on the UFT strategy to collapse BOW matrix to provide a lower-dimensional representation of documents instead of the words in a corpus. The quantitative evaluation shows that fuzzy clustering produces superior performance and features to Principal Components Analysis (PCA) and Singular Value Decomposition (SVD), two popular DR methods based on the UFT strategy