On interval-valued supra-fuzzy syntopogenous structure (Q1955272)

Summary: 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 \(\pi^X\).