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An Approach of Proximity in Rough Set Theory

Tiwari Surabhi, Singh Pankaj Kumar

Fundamenta Informaticae

2019

Vol. 166, nr 3

251--271

In this paper, we have constructed topological structures on rough sets by choosing the path of proximity relations on approximation spaces. So, by this virtue of purpose, we have used rough metric to define nearness concept between rough sets. Some basic results have been proved on this new nearness structure named as rough proximity. The study is well supported by examples. Finally, the theory is developed to construct the compactification of a rough proximity space.

Completion in a common supercategory of Met, UAP, wsAP and Near

Khare M., Tiwari S.

Demonstratio Mathematica

2013

Vol. 46, nr 1

209--227

This paper investigates the notion of approach nearness spaces. Using clusters, completion of an approach nearness space is constructed, which is a unified study of completion in the context of metric spaces, uniform approach spaces, weakly symmetric approach spaces and nearness spaces. Another generalization of completeness, called ultrafilter completeness is introduced to prove the Niemytzki–Tychonoff theorem for approach nearness spaces. Both definitions of completions are shown to be equivalent in a limit-regular approach space. Various examples are given to support the present study.