In this paper, we have studied the notion of nearness $d$-algebras which is a generalization BCK-algebras (or NBCK-algebra for short). Therefore, it defined that notions d$-subalgebra, d-ideal in $d$-algebras. Afterward, investigated relations among them and gave some examples.

The problem considered in this paper is the extension of an approximation space to include a nearness relation. Approximation spaces were introduced by Zdzisław Pawlak during the early 1980s as frameworks for classifying objects by means of attributes. Pawlak introduced approximations as a means of approximating one set of objects with another set of objects using an indiscernibility relation t...

The problem considered in this paper is the extension of an approximation space to include a nearness relation. Approximation spaces were introduced by Zdzis law Pawlak during the early 1980s as frameworks for classifying objects by means of attributes (features). Pawlak introduced approximations as a means of approximating one set of objects with another set of objects using an indiscernibilit...

Necessary and sufficient conditions on a nearness structure are provided for which the underlying topology is developable. It is also shown that a topology is developable if and only if it admits a compatible nearness structure with a countable base. Finally it is shown that a topological space is embeddable in a complete Moore space if and only if it admits a compatible nearness structure sati...

The aim of this study is to introduce nearness Γ-near ring, Γ-subnear ring and Γ-ideal. Moreover, some properties these structures are investigated.

A matrix nearness problem consists of finding, for an arbitrary matrix A, a nearest member of some given class of matrices, where distance is measured in a matrix norm. A survey of nearness problems is given, with particular emphasis on the fundamental properties of symmetry, positive definiteness, orthogonality, normality, rank-deficiency and instability. Theoretical results and computational ...

This paper studies the category theoretic aspects of ε-approach nearness spaces and ε-approach merotopic spaces, respectively, ε ∈ (0,∞], which are useful in measuring the degree of nearness (resemblance) of objects. Such structures measure the almost nearness of two collections of subsets of a nonempty set. The categories εANear and εAMer are shown to be full supercategories of various well-kn...

This paper presents an experiment with human subjects concerning the vague spatial relation ‘near’ in environmental space. After the topic is introduced and relevant previous work surveyed, the experiment is described. Three approaches to experimental analysis are presented and discussed: nearness neighbourhoods as regions with broad boundaries, fuzzy nearness and distance measures, and four-va...