闭模糊拟阵模糊圈的极值问题

The Extremum Problem of Fuzzy Circuits on Closed Fuzzy Matroids

本文主要方法是通过基本序列、导出拟阵序列和模糊集分解定理,将模糊圈的研究转化为对圈子集套和数组的研究。在闭模糊拟阵中,我们得出三个结论:以同一集合为支撑集的模糊圈的最大模糊圈总是存在;以同一子集串为圈子集套的模糊圈的最大模糊圈不一定存在。但是,找到了存在最大模糊圈的充要条件;以同一集合为支撑集的模糊圈的最小模糊圈,以同一子集串为圈子集套的模糊圈的最小模糊圈都是不存在的。但它们的最小模糊势是存在的,而且找出了计算最小模糊势的公式。我们构造了两个算法:一是构造支撑集最大模糊圈算法。通过这个算法可构造出支撑集最大模糊圈,同时计算出其最大模糊势;二是判断和构造圈子集套最大模糊圈算法。通过这个算法首先判断最大模糊圈是否存在,如果存在就可以找出圈子集套最大模糊圈同时计算出最大模糊势。

In closed fuzzy matroids, the article has three conclusions. First, maximum fuzzy circuits of the same support set always exist. Second, it is possible that there are maximum fuzzy circuits on the same circuit-subset sets. Moreover, the paper has found necessary and sufficient conditions about the existence of this maximum fuzzy circuits. Third, there are not minimum fuzzy circuits of the same support set or the same circuit-subset sets. However, the minimum fuzzy cardinality of these fuzzy circuits exist. A computational formula has given for the minimum fuzzy cardinality. This article has designed two algorithms. One is the algorithm of maximum fuzzy circuits about the same support set. With help of the algorithm, maximum fuzzy circuits can been got. In addition, its maximum fuzzy cardinality can been calculated. Another is the algorithm of maximum fuzzy circuits about the same circuit-subset sets. Have the aid of the algorithm, we can determine whether to there are maximum fuzzy circuits. When there are maximum fuzzy circuits, the algorithm can constructed maximum fuzzy circuits. Meanwhile, the algorithm can calculate the maximum fuzzy cardinality.