This work indicates application of the notion of fuzzy $$\alpha $$ -cut in rough set theory and studies the properties of Gödel-like arrow in details.
Biomedical named entity recognition is becoming increasingly important to biomedical research due to a proliferation of articles and also due to the current pandemic disease. This paper addresses the task of automatically finding and recognizing biomedical entity types related to COVID (e.g., virus, cell, therapeutic) with tolerance rough sets. The task includes i) extracting nouns and their co-occurring contextual patterns from a large BioNER dataset related to COVID-19 and, ii) annotating unlabelled data with a semi-supervised learning algorithm using co-occurence statistics. 465,250 noun phrases and 6,222,196 contextual patterns were extracted from 29,500 articles using natural language text processing methods. Three categories were successfully classified at this time: virus, cell and therapeutic. Early precision@N results demonstrate that our proposed tolerant pattern learner (TPL) is able to constrain concept drift in all 3 categories during the iterative learning process.
The theory of rough sets has been studied extensively, both from foundation and application points of view, since its introduction by Pawlak in 1982. On the foundations side, a substantial part of work on rough set theory involves the study of its algebraic aspects and logics. The present work is in this direction, initiated through the study of categories of rough sets. Starting from two categories RSC and ROUGH of rough sets, it is shown that they are equivalent. Moreover, RSC, and thus ROUGH, are found to be a quasitopos, a structure slightly weaker than topos. The construction is then lifted to a more general set-up to give the category RSC( $$\mathscr {C}$$ ) with an arbitrary non-degenerate topos $$\mathscr {C}$$ serving as a ‘base’, just as sets constitute a base for defining rough sets. The category-theoretic study gives rise to two directions of work. In one direction of work, a particular example of RSC( $$\mathscr {C}$$ ) when $$\mathscr {C}$$ is the topos of monoid actions on sets is considered. It yields the monoid actions on rough sets and that of transformation semigroups (ts) for rough sets, leading to decomposition results. A semiautomaton for rough sets is also defined. In the other direction, we incorporate Iwinski’s notion of ‘relative rough complementation’ in the internal algebra of the quasitopos RSC( $$\mathscr {C}$$ ). This results in the introduction of two new classes of algebraic structures with two negations, namely contrapositionally complemented pseudo-Boolean algebra (ccpBa) and contrapositionally $${\vee }$$ complemented pseudo-Boolean algebra (c $$\vee $$ cpBa). Examples of ccpBas and c $$\vee $$ cpBas are developed, comparison with existing algebras is done and representation theorems are established. The logics ILM and ILM- $$\vee $$ corresponding to ccpBas and c $${\vee }$$ cpBas respectively are defined, and different relational semantics are obtained. It is shown that ILM is a proper extension of a variant JP $$'$$ of Peirce’s logic, defined by Segerberg in 1968. The inter-relationship between relational semantics and the algebraic semantics of ILM and ILM- $${\vee }$$ are investigated. Lastly, in the line of Dunn’s study of logics, the two negations are expressed without the help of the connective of implication, and the resulting logical and algebraic structures are also studied.
In this article an attempt is made to introduce and study the notion of single-valued neutrosophic rough continuous mapping, single-valued neutrosophic rough compactness via single-valued neutrosophic rough topological spaces (SVNRTS). By defining the concept of single-valued neutrosophic rough continuous function, single-valued neutrosophic rough compactness, we formulate and discuss several interesting results on SVNRTSs.
This paper provides an overview of the Rough Set Database System (the RSDS for short) for creating bibliographies on rough sets and related fields, as well as sharing and analysis. The current version of the RSDS includes a number of modifications, extensions and functional improvements compared to the previous versions of this system. The system was made in the client-server technology. Currently, the RSDS contains over 38 540 entries from nearly 42 860 authors. This system works on any computer connected to the Internet and is available at http://rsds.ur.edu.pl .
