A Number Of Issues. Generalized Fuzzy Matrix Studies

In this paper, some special matrices over path algebra are studied. The main content con-sists of four chapters.In Chapter 1, we describe the relevant background, status of current research and the main work.In Chapter 2, we introduce some basic concepts including semiring, partial set, path alge-bra etc., and present some basic lemmas which will be used later.In Chapter 3, firstly, the indices and the periods of some generalized fuzzy matrices are estimated. Secondly, the structure of the sets of all the standard eigenvectors for a generalized fuzzy matrix with index is given, and it is proved that for a n x n generalized fuzzy matrix with index the set of all the standard eigenvectors of it coincides with the set of all the standard eigenvectors of its transitive closure. Finally, the stability of the orbits and the reduction of a generalized fuzzy matrix with index over path algebra are considered, some properties of the reduction are established.In Chapter 4. we discuss the transitivity of powers of a generalized fuzzy matrix with index.