Fuzzy clustering: insights and a new approach

Fuzzy clustering extends crisp clustering in the sense that objects can
belong to various clusters with different membership degrees at the same
time, whereas crisp or deterministic clustering assigns each object to a unique
cluster. The standard approach to fuzzy clustering introduces the so-called
fuzzifier which controls how much clusters may overlap. In this paper we
illustrate, how this fuzzifier can help to reduce the number of undesired local
minima of the objective function that is associated with fuzzy clustering.
Apart from this advantage, the fuzzifier has also some drawbacks that are
discussed in this paper. A deeper analysis of the fuzzifier concept leads us to
a more general approach to fuzzy clustering that can overcome the problems
caused by the fuzzifier.