This paper is devoted to a nearness relation in an Efremovic̆proximity space. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EFand a descriptive EFrelation. This leads to a study of the nearness of objects e...

In order to improve the validity and accuracy of fault diagnosis on mechanical equipment, this study applies fuzzy nearness approach by adjusting the traditional formulations. Besides, it points out the disadvantages in fault diagnosis of traditional nearness approach based on experimental data of gear transmission. A fuzzy nearness functionbased model is constructed to execute the fault diagno...

In this paper, our approach is to study properties of approximations on nearness approximation spaces. Afterwards, our aim is to define near semigroups and near ideals on near approximation spaces. We introduce some properties of these near structures. The nearness of sets and, in particular, the nearness of algebraic structures on nearness approximation spaces fits within the milieu of fuzzy s...

An artificial intelligence system that processes geothematic data would profit from a (semi-)formal or controlled natural language interface that incorporates concepts for nearness. Though there already exists logical-engineering approaches giving sufficient conditions for nearness relations, we show within a logical analysis that these suffer from some deficiencies. Non-engineering approaches ...

We provide a fairly general method, which is straightforward and widely applicable, for constructing some coreflections in the category of nearness frames. The method captures all coreflective subcategories with 1 1 coreflection maps; this includes the well-known uniform, totally bounded and separable coreflections. The primary application of this method answers in the affirmative the question ...

Nearness (a fuzzy nearness) is a fuzzy relation that can be used to model various grades of “being close” in a linear space. We study the uniform convergence of a sequence of functions with values in a space equipped with a nearness relation. The uniform convergence for the mappings into a space with a fuzzy nearness is defined and it is shown that a theorem similar to Moore-Osgood theorem for ...

Quasi-nearness biframes provide an asymmetric setting for the study of nearness; in [1] a completion (called a quasi-completion) was constructed for such structures and in [2] completeness was characterized in terms of the convergence of regular Cauchy bifilters. In this talk, questions of functoriality for this quasi-completion are considered and one sees that having enough regular Cauchy bifi...

An artificial intelligence system that processes geo-thematic data would profit from a (semi-)formal or controlled natural language interface that incorporates concepts for nearness. Though there already exists logical-engineering approaches giving sufficient conditions for nearness relations, we show within a logical analysis that these suffer from some deficiencies. Non-engineering approaches...

The problem considered in this paper is how to describe and compare visual objects. The solution to this problem stems from a consideration of nearness relations in two different forms of Efremovic̆ proximity spaces. In this paper, the visual objects are picture elements in digital images. In particular, this problem is solved in terms of the application of rough sets in proximity spaces. The ba...