Near sets. General theory about nearness of objects

Abstract 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 in character. The solution to the problem of approximating sets of perceptual objects results from a generalization of the approach to the classification of objects introduced by Zdzis law Pawlak's during the early 1980s. This generalization leads to the introduction of near sets. In addition, a formal explanation of the predicate near relative to near objects, near sets and nearness approximation spaces is given. The contribution of this paper is a formal basis for the discovery of perceptual objects that are qualitatively near each other. Mathematics Subject Classification: 03E75, 03E9