We use the framework of fractional calculus to quantify the linear viscoelastic properties of full-fat, low-fat, and zero-fat, semi-hard cheeses over a range of temperatures and water/protein ratios. These fractional constitutive models correctly predict the time-dependence and interrelation of the firmness, springiness, and rubberiness of these emulsion-filled hydrocolloidal gels. Our equations for the firmness F, springiness S, and rubberiness R, also correctly predict the effect of changing the magnitude or time-scale of the stress loading on the material even in the case of irreversible flow events, when cheese progressively transitions from a solid to a liquid. Finally we show how our FSR-equations can be used in a texture engineering context; they provide rational guidance to product reformulation studies and allow for extrapolation of a firmness measurement to practical situations in which the gel is subjected to prolonged creep loading.