直觉模糊等价矩阵构造方法

Method for Constructing Intuitionistic Fuzzy Equivalent Matrixes

对直觉模糊相似关系和等价矩阵构造问题进行了深入研究,提出一种利用求传递闭包来构造直觉模糊等价矩阵的方法,并从理论上给出了相关证明.首先,利用直觉模糊合成运算及其结合律,相关引理和数学归纳法证明了直觉模糊相似矩阵R的任意k次合成运算也是直觉模糊相似矩阵的定理.其次,综合运用直觉模糊最小传递矩阵的概念及相关引理,证明了n阶直觉模糊矩阵的传递闭包定理和n阶直觉模糊相似矩阵定理,推导出包含R的最小直觉模糊等价矩阵的推论.最后指出,可以从一个直觉模糊相似矩阵R出发,利用连续合成运算求传递闭包的方法来构造一个直觉模糊等价矩阵.

The issues of Intuitionistie Fuzzy （IF） resembling relations and the construction of IF equivalent matrixes get deeply into investigation, and a method for eonstructing IF equivalent matrixes by finding the transitive closure is proposed with a related proof in theory. The proof of a theorem, i.e. an IF resembling matrix via exertion of composition operations with any k-times is still an IF one, is first made out by utilizing composition operations on IFSs and the combo rules and a related lemma and the method of mathematical induction. Then, theorems of transitive closure of n-order IF matrix and resembling matrix are proven with a derived deduction on a minimum IF equivalent matrix with an inclusion R, by synthetically utilizing the fundamental notions of a minimum IF transitive matrix and a related lemma. Finally, a conclusion is presented that an intuitlonistic fuzzy equivalent matrix can be constructed out by using the techniques for finding transitive closure via a series of composition operations with limited times from an intuitionisfic fuzzy resembling matrix R.