Some properties of (r,s)-generalized fuzzy semi-closed sets and some applications

Abstract

In this work, the notion of \((r,s)\)-generalized fuzzy semi-closed sets is introduced and some properties are given. Also, we show that every \((r,s)\)-generalized fuzzy closed set by Abbas (2006) is \((r,s)\)-generalized fuzzy semi-closed set, but the converse need not be true. After that, the generalized forms of fuzzy continuous mappings between double fuzzy topological spaces \((X,\tau_{1}, \tau_{1}^*)\) and \((Y,\tau_{2}, \tau_{2}^*)\) are introduced and studied. Some interesting relationship between these mappings and other mappings introduced previously are investigated with the help of examples. In the end, the notion of \((r,s)\)-fuzzy GS-connected sets is introduced and studied with help of \((r,s)\)-generalized fuzzy semi-closed sets.