Maximal- and minimal symmetric solutions of fully fuzzy linear systems

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摘要

In this paper, we shall propose a new method to obtain symmetric solutions of a fully fuzzy linear system (FFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a FFLS (in the present paper, we assumed that the 1-cut of a FFLS is a crisp linear system or equivalently, the matrix coefficient and right hand side have triangular shapes), then some unknown symmetric spreads are allocated to each row of a 1-cut of a FFLS. So, after some manipulations, the original FFLS is transformed to solving 2n linear equations to find the symmetric spreads. However, our method always give us a fuzzy number vector solution. Moreover, using the proposed method leads to determining the maximal- and minimal symmetric solutions of the FFLS which are placed in a Tolerable Solution Set and a Controllable Solution Set, respectively. However, the obtained solutions could be interpreted as bounded symmetric solutions of the FFLS which are useful for a large number of multiplications existing between two fuzzy numbers. Finally, some numerical examples are given to illustrate the ability of the proposed method.

论文关键词:Fully fuzzy linear system (FFLS),Maximal symmetric solution,Minimal symmetric solution,Unites solution set (USS),Tolerable solution set (TSS),Controllable solution set (CSS)

论文评审过程:Received 2 March 2010, Available online 13 May 2010.

论文官网地址:https://doi.org/10.1016/j.cam.2010.05.009