Affiliations: Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, Univ. of Manitoba, E1-526, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada. jfpeters@ee.umanitoba.ca
Note: [] Many thanks to Andrzej Skowron, Som Naimpally, Homa Fashandi, Nick Peters, Maciej Borkowski, Amir Meghdadi, Surabhi Tiwari, Sheela Ramanna and the anonymous reviewers for their insights and suggestions concerning topics in this paper. I especially want to thank Homa Fashandi and Maciej Borkowski for their implementations of local admissible covers. This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 185986. Address for correspondence: Department of Electrical & Computer Engineering, Univ. of Manitoba, E1-526, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada
Abstract: This paper considers the nearness of sets in local descriptive admissible covers of nonempty sets and the problem of quantifying the nearness of such sets. A brief review of descriptive Efremovič spaces as well descriptive intersection and union provides a foundation for the study of descriptive admissible covers. Descriptively near sets in admissible covers contain sequences of points with members having similar descriptions. The motivation for this approach stems from the need to consider fine-grained neighbourhoods of points in admissible covers that facilitate highly accurate measures of nearness of tiny parts of sets of objects of interest. A practical application of local admissible covers is given in terms of micropalaeontology and the detection of minute similarities and differences in microfossils, useful in the study of climate change, mineral and fossil fuel exploration.
Keywords: Admissible cover, description, micropalaeontology, near sets, nearness, proximity space
