Optimality And Duality For Fuzzy Univex Programming

Decision makers usually take such complicated factors as technology, environment and competition into consideration to solve practical problems. And they more wish to use "more or less" rather than "yes or no" to answer optimization questions. Fuzzy pro-gramming is an important model and method for optimizing uncertain parameters. Fuzzy Set Theory can well build and solve optimization problems by setting lower objective func-tion goals and constraint conditions. And Fuzzy Mathematics and classical optimization methods together have stimulated various research directions and created plentiful research achievements.The fuzzification of generalized convex functions, optimality and duality for the fuzzy programming of fuzzy generalized convex functions are hot research issues in the field of fuzzy programming. Researchers have explored the fuzzification of convex functions and invex functions from different angles. The thesis aims at fuzzifying several types of gener-alized convex functions and giving optimality and duality results in the fuzzy programming. Based on existing research results, the author concludes and classifies fuzzification achieve-ments of convex functions, carries out the study on the fuzzification of invex functions and univex functions, and researches the optimality and duality of fuzzy weakly univex opti-mization and fuzzy univex optimization.Main work of the thesis includes:1. Compares definitions of fuzzy convex functions and proves their properties, propos-es definitions of fuzzy weakly invex functions and fuzzy invex functions and studies their properties. Results show that there are two ways for fuzzifying convex functions and invex functions, one way is convert fuzzy function to real functions by using two endpoint func-tions of a fuzzy function. The other way is using the operations under the scope of a fuzzy numbers. These two kinds of research results have advantages and disadvantages respec-tively. We call this two kind of fuzzifying generalized convex functions are fuzzy weakly generalized convex functions and fuzzy generalized convex functions.2. According to the definition of weak differentiable fuzzy function and two endpoint functions of the fuzzy function, the author puts forward fuzzy weakly univex function and studies its properties. Results show that, fuzzy convex function and fuzzy weakly invex function are special case of fuzzy weakly univex function. Then under the assumption of fuzzy weak differential functions, studies the optimality for the fuzzy programming whose objective function and constraint condition are fuzzy weakly univex function to obtain sev-eral sufficient conditions of the optimal solution and non-dominated solution for these fuzzy programming questions. Also duality for the fuzzy programming are studied.3. According to Principle of Zadeh’s extension principle and the operation of fuzzy numbers and fuzzy functions, the author puts forward the definition of interval valued uni-vex function and fuzzy univex function and studies its properties, Results show that, fuzzy convex function and fuzzy invex function are special case of fuzzy univex function, fuzzy weakly univex function and fuzzy univex function are different from each other. Then s-tudies the optimal conditions for the fuzzy programming whose objective function and con-straint condition are fuzzy univex function under the assumption of fuzzy g differentiable function to obtain several sufficient conditions of the optimal solution and non-dominated solution for these fuzzy programming questions. Also duality for the fuzzy programming are studied. And considering that optimal conditions for fuzzification are quite difficult to obtain, the author approximately represents the fuzzy optimization as the interval-valued optimization and gives the satisfactory solution of the original fuzzy optimization question by using the interval-valued optimization.