Approximation of Sets Based on Partial Covering

In this current paper we reveal a mathematical tool that helps us to comprehend certain natural phenomena. The main idea of this tool is a possible generalization of approximations of sets relying on the partial covering of the universe of discourse. Our starting point will be an arbitrary nonempty family B of subsets of an arbitrary nonempty universe U. On the analogy of the definition of Pawlak's type @s-algebra @s(U/@e) over a finite universe, let D"B denote the family of subsets of U which contains the empty set and every set in B and it is closed under unions. However, D"Bneither covers the universe nor is closed under intersections in general. Our notions of lower and upper approximations are straightforward point-free generalizations of Pawlak's same approximations which are imitations of the @e-equivalence class based formulations. Both of them belong to D"B. Our discussion will be within an overall approximation framework along which the common features of rough set theory and our approach can be treated uniformly. To demonstrate the relationship of our approach with natural computing, we will show an example relying on the so-called META program which is a recognition and evaluation program of the actual state of the natural and semi-natural vegetation heritage of Hungary.

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