An additive spectral method for fuzzy clustering is proposed. The method operates on a clustering model which is an extension of the spectral decomposition of a square matrix. The computation proceeds by extracting clusters one by one, which makes the spectral approach quite natural. The iterative extraction of clusters, also, allows us to draw several stopping rules to the procedure. This applies to several relational data types differently normalized: network structure data (the first eigenvector subtracted), affinity between multidimensional vectors (the pseudo-inverse Laplacian transformation), and conventional relational data including in-house data of similarity between research topics according to working of a research center. The method is experimentally compared with several classic and recent techniques and shown to be competitive.