Fuzzy Similar Matrix Equation X 2=X and the Existence of Optimal Fuzzy Equivalence Matrix
Fuzzy Similar Matrix Equation X 2=X and the Existence of Optimal Fuzzy Equivalence Matrix
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发表时间：
1999
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通讯作者：
L. Hong
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作者：
L. Hong
详细讨论了李红星提出的模糊相似矩阵方程X 2=X的解的结构。首先，提出模糊等价范式的概念来表达解。其次，指出了标准解析过程对应的参数系统的独特性。第三，给出了排列等价类和平移等价类的公式。第四，给出了解集的结构。最后证明了最优模糊等价矩阵的存在性。
The structure of the solution of fuzzy similar matrix equation X 2=X proposed by Li Hongxing is discussed in detail. First, the concept of fuzzy equivalent normal form is proposed in order to express the solutions. Second,the uniqueness of the parameter systems corresponding to standard resolution process is pointed out. Third, the formula about permutation equivalence classes and translation equivalence classes is given. Forth, the structure of the solution set is given. Finally, the existence of optimal fuzzy equivalence matrix is proved.