Semi-supervised clustering uses partially labeled data, as often occurs in practical clustering, to obtain a better clustering result. One approach uses hard constraints which specify data that must and cannot be within the same cluster. In this chapter, we propose another approach to semi-supervised clustering with soft pairwise constraints. The clustering method used is fuzzy c-means (FCM), a commonly used fuzzy clustering method. Two previously proposed variants, entropy- regularized relational/kernel fuzzy c-means clustering and indefinite kernel fuzzy c-means clustering algorithm are modified to use the soft constraints. In addition, a method is discussed that propagates pairwise constraints when the given constraints are not sufficient for obtaining the desired clustering result. Using some numerical examples, it is shown that the proposed algorithms obtain better clustering results.