On fuzzy relational equations and the covering problem
On fuzzy relational equations and the covering problem
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DOI：
10.1016/j.ins.2011.03.004
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
Jun-Lin Lin-Jun-Lin-Lin-38297248;Yan-Kuen Wu;S. Guu
中科院分区：
文献类型：
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作者：
Jun-Lin Lin-Jun-Lin-Lin-38297248;Yan-Kuen Wu;S. Guu
以往的研究表明，基于最大-连续阿基米德t-范数或最大-算术均值组合的模糊关系方程可以转化为覆盖问题，这是一个np困难问题。利用连续阿基米德t-范数和算术平均值的共同性质，将它们推广为“u-范数”，使基于最大-连续u-范数组合的FREs也可以转化为覆盖问题。本文还提出了一种将覆盖问题转化为最大积FREs的方法。因此，最大连续u范数FREs可以通过扩展求解覆盖问题或最大积FREs的任何方法来求解。
Previous studies have shown that fuzzy relational equations (FREs) based on either the max-continuous Archimedean t-norm or the max-arithmetic mean composition can be transformed into the covering problem, which is an NP-hard problem. Exploiting the properties common to the continuous Archimedean t-norm and the arithmetic mean, this study proposes a generalization of them as the “u-norm”, enabling FREs that are based on the max-continuous u-norm composition also to be transformed into the covering problem. This study also proposes a procedure for transforming the covering problem into max-product FREs. Consequently, max-continuous u-norm FREs can be solved by extending any procedure for solving either the covering problem or max-product FREs.