An ad-hoc wireless network has multihop architecture and is more mobile than single-hop network architecture in the real world. But the ad-hoc wireless network has some challenge with respect to mobility, real-time communication, routing path, maintenance, spatial reuse, bandwidth management, and packets broadcast overhead. This paper investigates two important issues to ensure more stable path routing and less re-clustering to improve the system performance. Novel Linked Stability-Based Clustering (LSC) and Linked Stability-Based Routing (LSR) algorithms, using fuzzy set theory, are proposed. The LSC algorithm guarantees the stability of the cluster to reduce the probability of re-clustering because the cluster-head is not easily replaced. The LSC algorithm proposed in this paper reduces the easy re-clustering problem of the HCC algorithm by considering not only connectivity but also the link's signal strength between the mobile nodes obtained from a fuzzy set in cluster-head determination. The membership function of the LSC algorithm, based on the link's signal strength, predicts a more stable link routing path using fuzzy set theory. Simulation results show that the proposed algorithm ensures the stability of the cluster and avoids unnecessary re-clustering; for example, the LSC algorithm occurs less frequently than LID and HC algorithms. Similarly, the LSR routing algorithm that uses fuzzy sets and membership functions is based on the mean signal strength and the relative movement between nodes, to obtain the lifetime of each connection and the path lifetime, from fuzzy inferences and fuzzy rules for reference. The LSR algorithm provides more reliable path lifetime and more stable transmission than the table-driven or on-demand approaches. Simulation results reveal that the path lifetime of the LSR algorithm is longer than that of DSR, with a lower probability of path drop and avoiding rerouting. The LSR algorithm has a higher mean number of hoppings, because it always finds the most suitable path and is more stable than DSR, without searching again for a new path when the paths drop.