Appendix A. Some basic definitions and operations of Fuzzy Set Theory
Some basic definitions of fuzzy sets from a mathematical perspective can be found in the following (Zadeh, 1965; Zimmermann, 2001):
Let U be a universe of discourse, a fuzzy set View the MathML source of U is characterized by a membership function View the MathML source, which associates with each element x of U and a number View the MathML source in the interval [0,1]. View the MathML source is denoted as View the MathML source.
Obviously, the characteristic function of ordinary set theory is a special case of the membership function. Let U be an ordinary set and X be the subset of U . The characteristic function of X can be defined as μx:U→[0,1].