Di-uniformities and Hutton uniformities


ÖZÇAĞ S., BROWN L. M., KRSTESKA B.

FUZZY SETS AND SYSTEMS, vol.195, pp.58-74, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 195
  • Publication Date: 2012
  • Doi Number: 10.1016/j.fss.2011.12.004
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.58-74
  • Hacettepe University Affiliated: Yes

Abstract

The authors characterize di-uniformities on a texture (S, J) in the sense of Ozgag and Brown (Di-uniform texture spaces, Appl. Gen. Top. 4(1) (2003), 157-192) in terms of functions on the texturing J. This characterization enables quasi-uniformities in the sense of Hutton (Uniformities on Fuzzy Topological Spaces, J. Math. Anal. Appl. 58 (1977) 559-571) to be regarded as di-uniformities on the corresponding Hutton Texture, thereby revealing di-uniformities as a generalization of Hutton quasi-uniformities. The effect of imposing a complementation on (S, J) is also considered and several important results established. (C) 2011 Elsevier B.V. All rights reserved.