Let \(R\) be a (left) near-ring and let \(\mu\) be a fuzzy subset of \(R\). Then \(\mu\) is called a fuzzy subnear-ring of \(R\) if \(\mu(x-y)\geq\min\{\mu(x),\mu(y)\}\) and \(\mu(xy)\geq\min\{\mu(x),\mu(y)\}\) for all \(x,y\in R\). \(\mu\) is a fuzzy ideal if \(\mu\) is a fuzzy subnear-ring and (a) \(\mu(x)=\mu(y+x-y)\), (b) \(\mu(xy)\geq\mu(y)\), (c) \(\mu((x+i)y-xy)\geq\mu(i)\) for all \(x,y,i\in R\). A fuzzy subnear-ring which satisfies (a) and (b) is called a fuzzy left ideal and a fuzzy subnear-ring which satisfies (a) and (c) is a fuzzy right ideal. If \(m\) is a fuzzy subset of \(R\), and \(0<t<1\), then the level set \(\mu_t\) is defined as \(\mu_t=\{x\in R\mid\mu(x)>t\}\). It is shown that if \(I\) is a left (right) ideal of a near-ring \(R\) and \(0<t<1\), then there exists a fuzzy left (right) ideal \(\mu\) of \(R\) such that \(I=\mu_t\). Moreover, two level left (right) ideals \(\mu_{t_1}\) and \(\mu_{t_2}\) of \(R\) are equal (with \(t_1<t_2\)) if and only if there is no \(x\in R\) such that \(t_1<\mu(x)<t_2\). Let \(R\), \(S\) be near-rings, and let \(f\colon R\to S\) be a near-ring homomorphism. If \(\mu\) is a fuzzy set in \(R\), then the image of \(\mu\) under \(f\) is the fuzzy set \(\nu\), defined by \(\nu(y)=\sup_{x\in f^{-1}(y)}\mu(x)\) for all \(y\in f(R)\). If \(\nu\) is a fuzzy set in \(f(R)\), the pre-image of \(\nu\) under \(f\) is the fuzzy set \(\mu=\nu\circ f\). It is shown that the pre-image of a left (right) ideal is a left (right) ideal. A fuzzy set \(\mu\) is said to have the sup property if for every subset \(T\) of \(R\) there exists \(t_0\in T\) such that \(\mu(t_0)=\sup_{t\in T}\mu(t)\). A homomorphic image of a fuzzy left (right) ideal having the sup property is a fuzzy left (right) ideal.