Abnormalization of anti fuzzy ideals in near-rings (Q2710498)

An anti fuzzy subnear-ring of a near-ring \(R\) is a fuzzy set \(\mu\) of \(R\) such that \(\mu(x-y)\leq\max(\mu(x),\mu(y))\), \(\mu(xy)\leq\max(\mu(x),\mu(y))\). An anti fuzzy ideal of \(R\) is an anti fuzzy subnear-ring \(\mu\) such that \(\mu(y+x-y)\leq\mu(x)\), \(\mu(xy)\leq\mu(y)\), \(\mu((x+z)y-xy)\leq\mu(z)\). The authors investigate some properties of these fuzzy sets. For example they prove that for any anti fuzzy ideal \(\mu\) of \(R\) and any increasing function \(f\colon[\mu(0),1]\mapsto[0,1]\) the fuzzy set \(\mu_f=f\circ\mu\) is an anti fuzzy ideal of \(R\).