This paper discusses a new class of matrix nearness problems that measure approximation error using a directed distance measure called a Bregman divergence. Bregman divergences offer an important generalization of the squared Frobenius norm and relative entropy, and they all share fundamental geometric properties. In addition, these divergences are intimately connected with exponential families...

Completeness for metric spaces is traditionally presented in terms of convergence of Cauchy sequences, and for uniform spaces in terms of Cauchy filters. Somewhat more abstractly, a uniform space is complete if and only if it is closed in every uniform space in which it is embedded, and so isomorphic to any space in which it is densely embedded. This is the approach to completeness used in the ...

A first—order axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for constructive topology.

Near sets are disjoint sets that resemble each other. Resemblance is determined by considering set descriptions defined by feature vectors (n-dimensional vectors of numerical features that represent characteristics of objects such as digital image pixels). Near sets are useful in solving problems based on human perception [44, 76, 49, 51, 56] that arise in areas such as image analysis [52, 14, ...

Krasner hyperrings are a generalization of rings. Indeed, in hyperring the addition is hyperoperation, while multiplication an ordinary operation. On other hand, rough set theory near theory. Now, this paper we interested combining these concepts. We study and investigate notion on nearness approximation space. Also, define subhyperring, hyperideal, homomorphism prove some results present sever...

In this article we present some mappings which can be used to measure the degree of inclusion of a set in a set and which characterize the binary relation of being-near-to, defined on finite sets of objects in line with Peters, Skowron, and Stepaniuk [12]. By means of these mappings, called inclusion functions in general, we extend the notion of nearness to the graded case where one can measure...