ε-Near Collections.

This paper considers the problem of how approach merotopic spaces can be used in the study of e-near collections of subsets. The solution to this problem, in general, stems from M. Katetov's observation that merotopic spaces are obtained by topologising certain parts of a nonempty set. In particular, a consideration of feature-based merotopic distance between collections of subsets in the context of approach spaces provides a means of quantifying the ε-nearness of collections within some ε ε (0,∞]. Using the proposed approach to measuring the nearness of collections, one can consider the merotopic distance between collections of fuzzy sets, or rough sets, or, for that matter, between collections of near sets, themselves. This opens the door to research concerning the degree of nearness of 'populations' of different types of sets. The contribution of this paper is an application of merotopies with two arguments in measuring the nearness of collections of open neighbourhoods in digital images.