Finite Chain Matrix Of Fuzzy Matrices

In this thesis, we devote to discuss the semiring of matrices over finite chain and the semiring of Fuzzy matrices. We study the index and period of the multiplicative semigroup of matrix over the finite chain and generalize the result obtained to Fuzzy matrix also. In addition, the period of some special Fuzzy matrix has been discussed.This dissertation consists of four chapters. Firstly, we introduce the background correlative and the origin of the thesis, also we show the main result. The second chapter includes the basic notations and conceptions. We introduce some concepts and theories related to poset and lattice, then we review the fundmental theory of semigroup and semiring. In chapter three, we investigate the matrix over the finite chain. Some homomorphisms of matrices semiring over finite chains have been presented and the decomposition of given matrix have been obtained. We prove the theorem about the index and period of multiplicative simigroup of matrix over finite chain. The final chapter mainly concerns about Fuzzy matrix. First we prove the index and period theorem of Fuzzy matrix which generalize the Kim's conclusion by using the result obtained in the third chapter. And next we discuss the period of which called strongly indecomposable Fuzzy matrix and obtain an important computing method which generalize the corresponding one of boolean matrix.