Topological extensions are closely related to nearness structures of various kinds. For example, the Smirnov compactification of a proximity space X is a compact Hausdorff space Y which contains X as a dense subspace and for which it is true that a pair of subsets of X is near if, and only if, their closures in Y meet. Lodato generalized this result to weaker conditions for the proximity and th...

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...

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

In this paper, we introduce a near set approach to image analysis. Near sets result from generalization of rough set theory. One set X is near another set Y to the extent that the description of at least one of the objects in X matches the description of at least one of the objects in Y. Near set Evaluation And Recognition (NEAR) system is used to measure the degree of resemblance between facia...

as mystics make relationships to god in different ways, they consider different aspects of his (god) characters. in this article, it is tried to verify distinct ways of mystics, relation to allah according to their conscience sentience (receipt) of gods traits (specifications). the main purpose of this article is surveying mystics’s relations and their inference to allah based on holly quran an...

Aligned corpora are often-used resources in CLIR systems. The three qualities of translation corpora that most dramatically affect the performance of a corpus-based CLIR system are: (1) topical nearness to the translated queries, (2) the quality of the alignments, and (3) the size of the corpus. In this paper, the effects of these factors are studied and evaluated. Topics of two different domai...