A general and easy computational method for functions of fuzzy numbers

Dong and Wong (1987) showed that the discretization method of Schmucker(1984) can give quite irregular and incorrect membership functions. The method of Dubois and Prade (1980) requires that the function be increasing over the solution space; and the nonlinear programming method of Baas and Kwakernaak (1977), although exact, requires very restrictive conditions, and its implementation is cumbersome except for the simplest algebraic functions. Therefore, the aim of the paper is to propose a general and easy computational method for functions of fuzzy numbers. We use the maximum (minimum) nonlinear programming method to derive the upper (lower) bound of the α-cut representation of fuzzy sets. Our nonlinear programming problem is to maximize (minimize) the combination of functions of fuzzy numbers, subject to the interval of the α-cut representation for functions of fuzzy numbers. The method has been implemented in a GINO package, and its results are general and efficient