Precise Sets in Approximation Spaces and Textures

Article type: Research Article

Authors: Dost, Şenol^{; *}

Affiliations: Hacettepe University, Department of Mathematics and Science Education, 06800 Beytepe, Ankara, Turkey. [email protected]

Correspondence: [*] Address for correspondence: Hacettepe University, Department of Mathematics and Science Education, 06800 Beytepe, Ankara, Turkey.

Abstract: In this paper, we propose the notion of precise sets in texture spaces. Precise sets are defined by using textural sections and presections under a direlation. We obtain some properties of definability; it is proved that the family of precise sets under reflexive and transitive direlation is an Alexandroff ditopology. It is observed that sections and presections, which are approximation operators in the textural meaning, are Galois connections. Finally, effective results are given for definability by using textural precise sets.

Keywords: Precise set, Definability, Texture space, Direlation, Approximation operator

DOI: 10.3233/FI-2018-1652

Journal: Fundamenta Informaticae, vol. 158, no. 4, pp. 353-368, 2018