Metric nearness refers to the problem of optimally restoring metric properties to distance measurements that happen to be non-metric due to measurement errors or otherwise. Metric data can be important in various settings, for example in clustering, classification, metric-based indexing, query processing and graph theoretic approximation algorithms. This paper formulates and solves the metric n...

The problem considered in this paper is the approximation of sets of perceptual objects that are qualitatively near each other. A perceptual object is either something presented to the senses or knowable by the mind. Objects that have the same appearance are considered qualitatively near each other, i.e., objects with matching descriptions. The term approximate means very near, in position or i...

Abstract The Alexandrov L -fuzzy nearness is a new addition to the systems that base for intelligent and its wide applications in various fields. This paper represents connections among such as: rough sets, semi-topogenous orders uniformities complete residuated lattices. Moreover, we show there Galois correspondence between categories of those mentioned systems.

The spatial expression “near” describes proximity and is frequently used for web search such as “gas stations near the old market”. What is “near” depends on the context and I investigate how a context dependent model for “near” can be formulated. For doing so, I investigate the following questions: (i) what is the relevant contextual information for “near”? (ii) how does the identified informa...