Related papers: Topologies and approximation operators induced by …
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…
We introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
Fuzzy rough set (FRS) has a great effect on data mining processes and the fuzzy logical operators play a key role in the development of FRS theory. In order to further generalize the FRS theory to more complicated data environments, we…
Soft set theory is an important and emerging area within soft computing, owing to its attribute-oriented mathematical framework and its wide applicability in diverse domains, including science and social sciences. The theoretical…
In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…
In this paper, we shall present a topological approach for the computation of some supremal sublanguages, often specified by language equations, which arise from the study of the supervisory control theory. The basic idea is to identify the…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
Local data structures are systems of neighbourhoods within data sets. Specifications of neighbourhoods can arise in multiple ways, for example, from global geometric structure (stellar charts), combinatorial structure (weighted graphs),…
The group of continuous binary operations on a topological space is studied; its relationship with the group of homeomorphisms is established. The category of binary $G$-spaces and bi-equivariant maps is constructed, which is a natural…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about…
The main purpose of this paper is to introduce and study the primal-proximity spaces. Also, we define two new operators via primal proximity spaces and investigate some of their fundamental properties. In addition, we obtain a new topology,…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
We have studied the concept of bipolarity of information in the soft sets. We have defined bipolar soft sets and basic operations of union, intersection and complementation for bipolar soft sets. Examples of bipolar soft sets and an…
Rough Set based Spanning Sets were recently proposed to deal with uncertainties arising in the problem in domain of natural language processing problems. This paper presents a novel span measure using upper approximations. The key…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…