Fuzzy Ideal Supra Topological Spaces

Abstract

In this paper, we introduce the notion of fuzzy ideals in fuzzy supra topological spaces. The concept of a fuzzy s-local function is also introduced here by utilizing the s-neighbourhood structure for a fuzzy supra topological space. These concepts are discussed with a view to find new fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated fuzzy supra topologies, and several relations between different fuzzy ideals and fuzzy supra topologies are also studied here. Moreover, we introduce a fuzzy set operator${\mathrm{\Psi }}_S$and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy$\ast$-supra dense-in-itself sets, fuzzy$S^{\ast }$-supra closedsets, fuzzy$\ast$-supra perfect sets, fuzzy regular-I-supra closedsets, fuzzy-I-supra opensets, fuzzy semi-I-supra opensets, fuzzy pre-I-supra opensets, fuzzy$\alpha$-I-supra opensets, and fuzzy$\beta$-I-supra opensets) and study some characteristics of these sets, and then, we introduce some fuzzy ideal supra continuous functions.