An investigation on Pythagorean fuzzy $$\mathfrak {F_{p}^*}$$ fraction dense space using Pythagorean fuzzy frames

Abstract

Abstract The concept of frame is a generalisation of the concept of category of topological space open subsets. As a result, each frame acts as an open set in this context and the Pythagorean fuzzy sets is defined as a frame. The primary goal of this research unit is to investigate the behaviour of Pythagorean fuzzy frames. Pythagorean fuzzy $$\mathfrak {F_{p}^*}$$ structure space is defined using Pythagorean fuzzy frames. Pythagorean fuzzy $$\mathcal {G^*}$$ closed sets, Pythagorean fuzzy dense set, Pythagorean fuzzy nowhere dense set, Pythagorean fuzzy somewhere dense set is established in order to investigate the Pythagorean fuzzy frames defined in Pythagorean fuzzy $$\mathfrak {F_{p}^*}$$ structure space. Further, Pythagorean fuzzy $$\mathfrak {F_{p}^*}$$ continuous function is explored in this manuscript. Separation axioms of the Pythagorean fuzzy $$\mathfrak {F_{p}^*}$$ structure space is established in order to comprehend the Pythagorean fuzzy frame. Additionally Pythagorean fuzzy $$\mathfrak {F_{p}^*}$$ fraction dense space and Pythagorean fuzzy $$\mathcal {P^*}$$ space is defined and explored to examine the behaviour of defined Pythagorean fuzzy frames.