Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming) > Nonlinear Programming

Fuzzy Programming Approach for Solving Multilevel Programming Problem

Author SongWei
Tutor ZhaoMaoXian
School Shandong University of Science and Technology
Course Applied Mathematics
Keywords Multilevel Programming Linear Bilevel Multi-follower Programming efficient solution satisfactory degree Fuzzy Programming algorithm Interactive Fuzzy Programming algorithm
CLC O221.2
Type Master's thesis
Year 2011
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In the modern decision-making systems, there are lots of systems with hierarchically characteristics. Many optimization problems of this complex system have been considered multilevel programming problems. So it is very important theoretic value and practical significance to study the properties and the solving algorithm of multilevel programming. The main work of this paper can be summarized as follows:The first chapter introduces the production and the development of the multilevel programming, the mathematical model, the research present situation, the production and the development of the fuzzy mathematics programming, and summarizes the main domain’s application and the algorithm of the multilevel programming. The second chapter mainly introduces the mathematical model of linear multilevel programming, basic concepts and theoretical properties, discusses and proves the equivalence between the effective solutions of the linear multilevel programming and the effective solutions of the corresponding fuzzy multi-objective programming. Finally, a fuzzy programming approach for solving linear multilevel programming is proposed. The proposed algorithm doesn’t consider variables’ satisfactory degrees to avoid the complexity of the calculation and inconsistencies. In the third chapter firstly presents the linear bilevel multi-follower programming problem’s general form through describing the real existence. Then a fuzzy programming algorithm which different from the method of Lai et al. is given. Lai et al. advocate considering fuzzy goals and decision variables satisfactory degree, the algorithm in this chapter is just considering the fuzzy goal satisfactory degree. A numerical example is given to illustrate the process of the algorithm and the feasibility of the presented approach. In order to make the satisfactory balance between the upper decision maker and each lower decision maker, an interactive fuzzy programming algorithm is proposed. Illustrative numerical examples are provides to demonstrate the feasibility. The fourth chapter summarizes the obtained results and prospects the future work.

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