Unsupervised clustering of a set of data items of an arbitrary model into clusters which comply with an arbitrary model of homogeneity is a useful tool in many applications within the general field of computer sciences. This problem, however, is in essence ill-posed, due to the fact that it concerns the determination of cluster representations as well as data item-to-cluster correspondences, two entities which are heavily entangled. The research community is well aware of this ambiguity and has responded with several important contributions, such as the fuzzy membership regime and varied approaches to robustification, among others. Some of these works, however, utilize models and parameters which are in essence based on the intuition of the researchers and require the deliberate adjustment of regularization coefficients and configuration parameters which are defined metaphorically. In this work, we utilize a derivation-based approach and perform Bayesian loss modeling in order to derive the objective function for a fuzzy clustering algorithm which utilizes weighted data. The third component of the solution explored in this paper, which to the best of our knowledge is novel to this work, is the utilization of relevance factors for the clusters. We demonstrate that it is possible to avoid the necessity for knowing the number of clusters present in a set of data items a priori through replacing $C$, the number of clusters in traditional fuzzy clustering, with a maximum bound. This framework is possible because the developed algorithm utilizes fuzzy cluster relevant factors which evolve during the progression of the clustering solution and therefore yield the most relevant clusters to the input set of data items at convergence.