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Figure 2.5.
Fuzzy sets
Ã
and
represented by trapezoidal membership
functions.
Figure 2.6.
Operations between two fuzzy sets: (a) union, (b) intersection, and
(c) complement.
A fuzzy set defined by a normal as well as convex fuzzy set is called a fuzzy number (see
Appendix I for definitions). It is to be noted that the union and intersection operations
may result in a non-normal and non-convex fuzzy set. Therefore, the operations on fuzzy
numbers are normally carried out by fuzzy arithmetic. The rules of fuzzy arithmetic are
based on the Extension Principle of fuzzy set theory. The Extension Principle for
operations on fuzzy numbers is described in detail in Subsection 3.2.1, and the
derivations for the basic fuzzy arithmetic are presented in Appendix I.
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