  The limited version of bisimulation, called limited approximate bisimulation,
has recently been introduced to fuzzy transition systems (NFTSs). This article
extends limited approximate bisimulation to NFTSs, which are more general
structures than FTSs, to introduce a notion of $k$-limited
$\alpha$-bisimulation by using an approach of relational lifting, where $k$ is
a natural number and $\alpha\in[0,1]$. To give the algorithmic
characterization, a fixed point characterization of $k$-limited
$\alpha$-bisimilarity is first provided. Then $k$-limited $\alpha$-bisimulation
vector with $i$-th element being a $(k-i+1)$-limited $\alpha$-bisimulation is
introduced to investigate conditions for two states to be $k$-limited
$\alpha$-bisimilar, where $1\leq i\leq k+1$. Using these results, an
$O(2k^2|V|^6\cdot\left|\lra\right|^2)$ algorithm is designed for computing the
degree of similarity between two states, where $|V|$ is the number of states of
the NFTS and $\left|\lra\right|$ is the greatest number of transitions from
states. Finally, the relationship between $k$-limited $\alpha$-bisimilar and
$\alpha$-bisimulation under $\widetilde{S}$ is showed, and by which, a logical
characterization of $k$-limited $\alpha$-bisimilarity is provided.

Dynamical Systems