Basics of fuzzy sets

Abstract

In this chapter we summarize basic knowledge on fuzzy logics and fuzzy sets. After a short historical overview of ideas strongly connected to and preceding the notion of fuzzy logics and fuzzy sets, we outline links between many-valued and fuzzy logics. Then fuzzy subsets of a universe are introduced. Interpretations of unary and binary connectives in fuzzy logics as appropriate functions (operations) on the unit interval are central to the approach. Fundamental knowledge on these function classes is presented then, including results on triangular norms and conorms, as well as on implications. Our concluding remarks suggest further reading, beyond the basics.