ABSTRACT
This chapter is devoted to a brief discussion of those topics in fuzzy sets and models that are germane to fuzzy clustering. Fuzzy models are the primary tool for representation of linguistic imprecision. The basic idea of fuzzy sets is easy to grasp. Fuzzy memberships represent similarities of objects to imprecisely defined properties, while probabilities convey information about relative frequencies. When relative frequencies of chance occurrences are important, models should reflect this information. But when uncertainty is non-statistical, fuzzy models may offer a more natural and useful alternative. It is hard to guess if the argument between the fuzzy and probabilistic camps will ever subside entirely. Successful use of fuzzy models in many real-world engineering applications has rendered this a moot debate for all but the most philosophically inclined and scientifically narrow-minded.
