Method for Constructing Intuitionistic Fuzzy Equivalent Matrixes
直觉模糊等价矩阵构造方法

The issues of Intuitionistic Fuzzy(IF) resembling relations and the construction of IF equivalent matrixes get deeply into investigation,and a method for constructing 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 intuitionistic 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 intuitionistic fuzzy resembling matrix R.