Brief Introduction to Fuzzy Sets

We present a brief introduction to fuzzy sets theory for the interested readers who has not yet been exposed to this area. Particular emphasis is on basic elements and definitions, and to those which are relevant for the topics covered by this volume. First, the concept of a fuzzy set is presented as a formal means for dealing with the imprecision of meaning, caused mainly by the use of a natural language; such an imprecision is meant to be related to a gradual membership of elements. This is followed by main operations on fuzzy sets, the concepts of cardinality, a fuzzy relation, etc. Then, the concept of a fuzzy number is sketched. Basic operations on fuzzy numbers are dealt with with emphasis on the practically most relevant case of triangular and/or trapezoid fuzzy numbers.