On Interval-Valued Supra-Fuzzy Syntopogenous Structure

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 S, there is another interval-valued fuzzy syntopogenous structure S-c called the conjugate of S. 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 X will be denoted by I-X and the family of all interval-valued fuzzy sets on a nonempty set X will be denoted by pi(X).