ABSTRACT
This chapter presents the basic theory of fuzzy logic, which uses the concept of fuzzy sets. Compositional rule is what is applied for making inferences in decision making associated with fuzzy logic. A fuzzy set may be represented by a membership function. This function gives the grade of membership within the set, of any element of the universe of discourse. The membership function maps the elements of the universe onto numerical values in the interval. Composition can be interpreted as a matching of two fuzzy sets, and making an inference according to the result. The concept of Cartesian product can be directly extended to more than two fuzzy sets. The extension principle was introduced by Lotfi A. Zadeh to give a method for extending standard mathematical concepts to their fuzzy counterparts. The extension principle is used to map one fuzzy set onto another fuzzy set through a crisp function.
