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On the Discussion of Fuzzy Approximate Solutions for Some Kinds of Fully Fuzzy Linear Systems

Author: LiuKun
Tutor: GongZengTai
School: Northwest Normal University
Course: Applied Mathematics
Keywords: Generalized LR-fuzzy Numbers Fuzzy Approximate Solution Fully Fuzzy Linear System(FFLS)
CLC: O159
Type: Master's thesis
Year: 2009
Downloads: 24
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Abstract


In the mathematical modeling of mathematics, physics, engineering computation and statistical analysis, the useful and easily estimated method is that it could be transferred into a linear system in some sense. However, the uncertainty of the parameters is involved in the process of actual mathematical modeling, which is often represented as fuzzy numbers. So the investigation of solving the solutions for fuzzy linear systems whose elements of coefficient matrix or augmented matrix are fuzzy numbers, plays an important role in the fuzzy mathematics theory. In this thesis, the fuzzy approximate solution and its computation methods for some kinds of fully fuzzy linear systems are investigated.Firstly, the concept of the LR-fuzzy numbers is expanded, and the generalized LR-fuzzy numbers is defined. The approximate expressions of the fuzzy number arithmetic operations are given. Secondly, the non-negative and non-position fuzzy approximate solutions of the fully fuzzy linear system are discussed, and the judge theorem of its solutions is obtained. Furthermore, two special kinds of fully fuzzy linear systems including the fuzzy linear system and the homogenous fuzzy linear system are studied. A judge theorem of its solutions and a general solution representation for the fuzzy linear system and the homogenous fuzzy linear system are shown, respectively. In additions, a generalized consistent and inconsistent fully fuzzy linear system are further defined by using the relation between the ranks of coefficient matrix and augmented matrix. The fuzzy approximate solution, the fuzzy approximate general solution, the fuzzy least squares approximate and the fuzzy minimum least squares approximate solution about them are discussed. Finally, the dual fully fuzzy linear system is defined, its fuzzy approximate solution is discussed, and the Cramer ruler method of dual fully fuzzy linear system is pointed out. Both direct method and Cramer method are also obtained and compared by an example.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
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