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...

The system of administrative units for a state like Switzerland can be formally described by a totally ordered set of nested partitions where, e.g., the municipalities make up a finer partition than the partition induced by districts. Based on these partitions one can define binary non-symmetric nearness relations between regions in which the second argument determines the granularity (or the s...

In gb, the importance of phrase-structure rules has dwindled in favour of nearness conditions. Today, nearness conditions play a major role in defining the correct linguistic representations. They are expressed in terms of special binary relations on trees called command relations. Yet, while the formal theory of phrase-structure grammars is quite advanced, no formal investigation into the prop...

Given a square matrix with noisy dissimilarity measures between pairs of data samples, the metric nearness model computes best approximation from set valid distance metrics. Despite its wide applications in machine learning and processing tasks, faces non-trivial computational requirements seeking solution due to large number constraints associated feasible region. Our work designed practical a...