Fuzzy rational approximation of irrationals (Q1037924)

Let \({\mathcal D}=\{(p,q):q\in{\mathbb N},\,p\in\{0,1,\ldots,q\}\}\). The authors define a fuzzy interval with rational core as a function \(f_{(p,q)}:[0,1]\to[0,1] \), \((p,q)\in {\mathcal D}\), such that \(f_{(p,q)}\) is non-decreasing in \([0,p/q)\), non-increasing in \((p/q,1]\) and \[ f_{(p,q)}(x)=1\quad\text{if}\quad x=\tfrac{p}{q}, \] \[ f_{(p,q)}(x)=0\quad\text{if}\quad | x-\tfrac{p}{q}|\geq \theta(q) \] and discuss the approximation of irrational numbers by such functions.