Fuzzy monotone functions and applications

The grade of membership function for fuzzy monotone functions is defined an d investigated. An algorithm for finding the membership value is presented. A minterm even function and minterm odd function are defined and studied. It is found that these two functions are the two most alternation functions . The relationships with threshold functions are also presented. In additio n, three ways to implement a fuzzy monotone increasing function are investi gated. Applications to function representation, data compression and error detection are illustrated. The results have useful applications in fuzzy lo gic, expert systems, fuzzy expert systems, and also management of uncertain ty.