Fuzzy Functions

Abstract

Just as crisp function are important in mathematical modeling, fuzzy functions are important in fuzzy modeling. The usual way to obtain a fuzzy function is to extend a crisp function to map fuzzy sets to fuzzy sets, and there are two common methods to accomplish this extension. The first method, called the extension principle procedure, is discussed in the next section, and the second method, called the α-cut and interval arithmetic procedure, is presented in section three. In a pre-calculus course you study different classes of functions including linear, quadratic, polynomial, radical, exponential and logarithmic and we do this for fuzzy functions in section four. Fuzzy trigonometric functions are in Chapter 10. Also in pre-calculus you would study inverse functions and section five is about fuzzy inverse functions. Elementary differential calculus of fuzzy functions is introduced in the last section, section six.