On The Convex Fuzzy Optimization In The Quotient Space Of Fuzzy Numbers And Its Application

In this thesis, on the basis of fuzzy optimization theory and the latest results, the fuzzy optimizations of convex fuzzy mappings in the quotient space of fuzzy numbers are discussed.Firstly, the gradient and Hessian matrix of fuzzy mappings in the quotient space of fuzzy numbers are defined by the midpoint functions. By considering an ordering relation on the quotient space of fuzzy numbers, the concepts of convexity, quasiconvexity and pseudoconvexity for fuzzy mappings and their properties are proposed.Secondly, two kinds of solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers are introduced with respected to the comparability of objective functions based on a partial ordering relation. Under these settings, the fuzzy optimizations and KKT optimality conditions are elicited naturally by introducing the Lagrange function multipliers, and we also provide some numerical examples to illustrate the main results.Finally, an application in the control production systems based on the convex fuzzy optimizations in the quotient space of fuzzy numbers is provided.