Finding the complete set of minimal solutions for fuzzy relational equations with max-product composition
Finding the complete set of minimal solutions for fuzzy relational equations with max-product composition
复制标题
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Yan-Kuen Wu;S. Guu
中科院分区：
文献类型：
--
作者：
Yan-Kuen Wu;S. Guu
众所周知，具有极大积组合的模糊关系方程的解集可以由最大解和有限个最小解确定。最大解的解析表达式是存在的，而且很容易得到，但是求最小解的完备集却不是一件容易的事。本文首先从最大解的角度给出了任意最小解的一个必要条件。精确地说，任意最小解的每个非零分量取最大解的对应分量的值。然后，我们提出规则来减少问题，这样就可以很容易地找到解决方案。给出了一个数值例子来说明我们的方法。
It is well known that the solution set of fuzzy relational equations with max-product composition can be determined by the maximum solution and a finite number of minimal solutions. There exists an analytic expression for the maximum solution and it can be yielded easily, but finding the complete set of minimal solutions is not trivial. In this paper we first provide a necessary condition for any minimal solution in terms of the maximum solution. Precisely, each nonzero component of any minimal solution takes the value of corresponding component of the maximum solution. We then propose rules to reduce the problem so that the solution can easily be found. A numerical example is provided to illustrate our procedure.