Fuzzy c-means

The first algorithm that we will propose is a variation of k-means that's based on soft assignments. The name Fuzzy c-means derives from the concept of a fuzzy set, which is an extension of classical binary sets (that is, in this case, a sample can belong to a single cluster) to sets based on the superimposition of different subsets representing different regions of the whole set. For example, a set based on the age of some users can have the degrees young, adult, and senior, associated with three different (and partially overlapping) age ranges: 18-35, 28-60, and >50. So, for example, a 30-year-old user is both young and adult, to different degrees (and, indeed, is a borderline user, considering the boundaries). For further details about these kinds of sets and all of the related operations, I suggest the book Concepts and Fuzzy Logic, Belohlavek R., Klir...