Related papers: On a Well-behaved Relational Generalisation of Rou…
Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to…
In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and…
We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…
A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…
In [P. Majumdar, S. K. Samanta, Similarity measure of soft sets, New Mathematics and Natural Computation 4(1)(2008) 1-12], the authors use matrix representation based distances of soft sets to introduce matching function and distance based…
Relation extraction aims to identify the target relations of entities in texts. Relation extraction is very important for knowledge base construction and text understanding. Traditional binary relation extraction, including supervised,…
In this paper, the definition of fuzzy rough relation on a set will be introduced and then it would be proved that the collection of such relations is closed under different binary compositions such as, algebraic sum, algebraic product etc.…
The paper is the second of our series of notes aimed to bring back in circulation some bright ideas of early modern set theory, mainly due to Harrington and Sami, which have never been adequately presented in set theoretic publications. We…
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Graph-based frames have been introduced as a logical framework which internalizes an inherent boundary to knowability. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results…
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris 7, March…
In this paper we give a characterisation of trivial extension algebras in terms of quivers with relations. This result is based on a explicit description of the ideal of relations of the trivial extension of an algebra, given by the first…
We consider tolerances $T$ compatible with an equivalence $E$ on $U$, meaning that the relational product $E \circ T$ is included in $T$. We present the essential properties of $E$-compatible tolerances and study rough approximations…
Relative smoothness and strong convexity have recently gained considerable attention in optimization. These notions are generalizations of the classical Euclidean notions of smoothness and strong convexity that are known to be dual to each…