In　this　paper,　generalized　fuzzy　matrices　are　considered　as　matrices　over　a　special　type　of　semiring　which　is　called　path　algebra.　Some　properties　and　characterizations　for　generalized　fuzzy　matrices　with　periods　are　established　and　an　expression　for　the　transitive　closure　of　a　generalized　fuzzy　matrix　with　a　period　as　a　sum　of　its　powers　is　shown.　Reduction　of　generalized　fuzzy　matrices　is　defined　and　some　properties　for　reduction　of　generalized　fuzzy　matrices　with　periods　are　obtained.　Also,　the　structure　of　all　standard　eigenvectors　for　a　generalized　fuzzy　matrix　with　a　period　is　determined.　©　2011　Elsevier　B.V.　All　rights　reserved.