| In the real word, there are many optimization models in uncertain environment.Fuzzy mathematical programming is an effective tool to deal with such optimization models. In this thesis we mainly investigate the fully fuzzy linear programming, fuzzy relation system and fuzzy relation mathematical programming. Based on the practical application background, we propose several fuzzy optimization problems, which are solved by effective algorithms and illustrated by some numerical examples.Section 1 is a preface, in which we take an overview of fuzzy linear programming, fuzzy relation system and fuzzy relation mathematical programming. Besides,motivation of the investigation, main content and novelty of the thesis are introduced in this section.In Section 2, we investigate two kinds of fully fuzzy linear programming. Linear programming with all coefficients and variables represented by fuzzy numbers is said to be fully fuzzy linear programming(FFLP). For FFLP with LR fuzzy parameters, we define an order relation on the set of all LR flat fuzzy numbers. Based on the defined order relation, the FFLP can be converted into a crisp multi-objective linear programming equivalently before it is solved. For FFLP with triangular fuzzy parameters and flexible constraints, we define a novel order relation with possibility by using the expected value and interval. Flexible constraints are converted into constraints with possibility before solving the original problem based on the defined order relation.In Section 3, after introducing some application background of max-product fuzzy relation system, we provide structure and properties of the solution set as well as the resolution method. For the P2 P wireless communication base-station system,when considering the priority grade of the basic stations, we define the lexicography minimum solution of max-product fuzzy relation inequalities or equations. Corresponding solution algorithm is proposed step by step and illustrated by numerical examples. Besides, fuzzy relation minimax programming with max-product composition operator is established when the priority grade of the basic stations goes beyond consideration. Algorithm for solving the corresponding fuzzy relation minimax programming is presented in detail. While for the P2 P wireless network system, in order to decrease the dissatisfaction degree of the terminals, we establish and investigate the semi-latticized fuzzy relation geometric programming with max-product composition operator.In Section 4, we mainly study the addition-min fuzzy relation system and its optimization problem. As shown in the recent literatures, a P2 P file sharing system could be reduced into a group of addition-min fuzzy relation inequalities. In order to decrease the network congestion and improve the running efficiency in such system,we study the corresponding optimization problem with and without consideration of the priority grade of the terminals, respectively. When considering the priority grade of the terminals, we discuss the lexicography minimum solution of addition-min fuzzy relation inequalities. On the other hand, when it is unnecessary to consider the priority grade, fuzzy relation minimax programming problem with addition-min composition operator is introduced to describe the optimization model in such system. SingleVariable-Programming method and Optimal-Vector-Based method are developed to deal with the proposed problem respectively. When the minimal solution of the constraint is not unique, the Optimal-Vector-Based method can be used to find a minimal optimal solution, but the Single-Variable-Programming method can only be used to find the maximum optimal solution.Section 5 is the conclusion and future work. In this section, we summarize the main contents in this thesis. Besides, some subsequent researching topics are presented for future work. |
