Textures and Fuzzy Rough Sets

Diker M.

FUNDAMENTA INFORMATICAE, cilt.108, ss.305-336, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 108
  • Basım Tarihi: 2011
  • Doi Numarası: 10.3233/fi-2011-425
  • Dergi Adı: FUNDAMENTA INFORMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.305-336
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.