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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 854942, 8 pages
Research Article

On Interval-Valued Supra-Fuzzy Syntopogenous Structure

Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Received 12 August 2012; Accepted 1 November 2012

Academic Editor: Hamid Reza Karimi

Copyright © 2012 F. M. Sleim and Heba I. Mustafa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new definition of interval-valued supra-fuzzy syntopogenous (resp., supra-fuzzy proximity) space is given. We show that for any interval-valued fuzzy syntopogenous structure , there is another interval-valued fuzzy syntopogenous structure called the conjugate of . This leads to introducing the concept of interval-valued bifuzzy syntopogenous space. Finally, we show every interval-valued bifuzzy syntopogenous space induces an interval-valued fuzzy supra-syntopogenous space. Throughout this paper, the family of all fuzzy sets on nonempty set will be denoted by and the family of all interval-valued fuzzy sets on a nonempty set will be denoted by .