Service-based systems (SBSs) need to be reconfigured when there is evidence that the selected Web services configurations no further satisfy the specifications models and, thus the decision-related models will need to be updated accordingly. However, such updates need to be performed at the right pace. On the one hand, if the updates are not quickly enough, the reconfigurations that are required may not be detected due to the obsolescence of the specification models used at runtime, which were specified at design-time. On the other hand, the other extreme is to promote premature reconfiguration decisions that are based on models that may be highly sensitive to environmental fluctuations and which may affect the stability of these systems. To deal with the required trade-offs of this situation, this paper proposes the use of linguistic decision-making (LDM) models to represent specification models of SBSs and a dynamic computing-with-words (CWW) architecture to dynamically assess the models by using a multi-period multi-attribute decision making (MP-MADM) approach. The proposed solution allows systems under dynamic environments to offer improved system stability by better managing the trade-off between the potential obsolescence of the specification models, and the required dynamic sensitivity and update of these models.