Textures and Fuzzy Rough Sets

Diker M.

FUNDAMENTA INFORMATICAE, vol.108, pp.305-336, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 108
  • Publication Date: 2011
  • Doi Number: 10.3233/fi-2011-425
  • Title of Journal : FUNDAMENTA INFORMATICAE
  • Page Numbers: pp.305-336

Abstract

In this paper, we consider the Alexandroff topology for texture spaces. We prove that there exists a one-to-one correspondence between the Alexandroff ditopologies, and the reflexive and transitive direlations on a given texture. Using textural fuzzy direlations on a fuzzy lattice, we obtain a fuzzy rough set algebra where the inverse fuzzy relation and inverse fuzzy corelation are the upper approximation and lower approximation, respectively. In a special case, this gives us the fuzzy rough sets which are calculated with respect to the min-t norm introduced by S. Gottwald, or the fuzzy rough sets which are considered by D. Pei.