Spline membership function and its application in multiple objective fuzzy control problem

Abstract In fuzzy decision theory, first introduced by Bellman and Zadeh in 1970, the use of linear membership functions is well established. The rate of change in the degree of membership need not, in general, be constant, particularly in time dependent problems or situations where it is considered as a criterion. The idea of normalized spline membership function and normalized basis spline membership function is introduced here. It is observed that the fuzzy decision operator corresponding to the fuzzy alternatives can be expressed in terms of these proposed membership functions. A new method of solution in a multistage form is discussed for the general non-linear multiple objective fuzzy control problem. The application of normalized spline membership function in the multiple objective fuzzy control problem is illustrated with a numerical example.