An introduction to fuzzy systems.

We introduce the notion of fuzzy sets as a tool for modeling sets with ill-defined or flexible boundaries. Fuzzy sets naturally appear when describing the meaning of natural language words pertaining to quantitative scales, or when modelling the notion of typicality. The three main semantics for fuzzy sets are recalled: similarity, preference and uncertainty. Each semantics underlies a particular class of applications. Similarity notions are exploited in clustering analysis and fuzzy controllers. Uncertainty is captured by fuzzy sets in the framework of possibility theory. The membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems. Fuzzy sets are acknowledged as a major tool in information engineering for the purpose of bridging the gap between human-originated formalized knowledge, and numerical data.