Nowadays practical solutions of engineering problems involve model-integrated computing. Due to their flexibility, robustness, and easy interpretability, the application of fuzzy models, may have an exceptional role. Despite of their advantages, the usage is still limited by their exponentially increasing computational complexity. Although, combining fuzzy and anytime techniques it becomes possible to cope with the available, usually imperfect or even missing information, the dynamically changing, possibly insufficient amount of resources and reaction time. In this paper, possibilities offered by (Higher Order) Singular Value Decomposition ((HO)SVD) based anytime fuzzy models are analyzed. A modeling methodology is suggested, which offers a way for both complexity reduction and improvement of the accuracy without complexity explosion thus coping with the temporarily available amount of information and (finite) time/resources and finding the balance between accuracy and complexity.