Extremal Theory Of Fuzzy-valued Function And It’s Application

Extreme of fuzzy-valued function was not thoroughly researched until people resolved theanalytical expression of fuzzy-valued functions. According to this problem, this paper obtainesresearch results as follows:First of all, this paper researches convexity of fuzzy-valued function by defining thegeneralized fuzzy arithmetic with inequality constraint, the properties of convex fuzzy-valuedfunction are also analysed, author gives the judgment method of monotonicity and convexity offuzzy-valued function. Meanwhile, this paper presents adjoint function of fuzzy-valued functionby defining the structured sequence of fuzzy numbers, and gives the definition of adjointmonotonicity of fuzzy-valued function and the definition of adjoint convexity of fuzzy-valuedfunction, this paper also researches the properties of adjoint convex fuzzy-valued function, aswell as the judgment method of adjoint monotonicity and adjoint convexity.Secondly, this paper proves that the research of extreme of fuzzy-valued function can betransformed into general extreme of its adjoint function. This paper not only presents the conceptof generalized extreme of fuzzy-valued function, but also gives the methods for solving thegeneralized extreme value and generalized extreme points.Last but not the least, in this paper, the theories of extreme of fuzzy-valued function areapplied to the solutions of fuzzy inventory models.