The deterministic annealing (DA) and simulated annealing (SA) methods are well combined as DASA. By regularizing the fuzzy c-means method with the fuzzy entropy, the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained as a membership function, and, while optimizing its parameters by SA, the minimal of the Helmholtz free energy for fuzzy c-means clustering is searched by DA. Since shapes of membership functions obtained by DASA are very rough, it is important to interpolate them. Thus, interpolation is introduced to DASA and shows its effectiveness by a numerical experiment.